1. CMB Online first
 Efrat, Ido; Matzri, Eliyahu

Vanishing of Massey products and Brauer groups
Let $p$ be a prime number and $F$ a field containing a root of
unity of order $p$.
We relate recent results on vanishing of triple Massey products
in the mod$p$ Galois cohomology of $F$,
due to Hopkins, Wickelgren, MinÃ¡Ä, and TÃ¢n, to classical
results in the theory of central simple algebras.
For global fields, we prove a stronger form of the vanishing
property.
Keywords:Galois cohomology, Brauer groups, triple Massey products, global fields Categories:16K50, 11R34, 12G05, 12E30 

2. CMB Online first
 Edmunds, Charles C.

Constructing Double Magma on Groups Using Commutation Operations
A magma $(M,\star)$ is a nonempty set with a binary
operation. A double magma $(M, \star, \bullet)$ is a
nonempty set with two binary operations satisfying the
interchange law,
$(w \star x) \bullet (y\star z)=(w\bullet y)\star(x \bullet
z)$. We call a double magma proper if the two operations
are distinct and commutative if the operations are commutative.
A double semigroup, first introduced by Kock,
is a double magma for which both operations are associative.
Given a nontrivial group $G$ we define a system of two magma
$(G,\star,\bullet)$ using the commutator operations $x \star
y = [x,y](=x^{1}y^{1}xy)$ and $x\bullet y = [y,x]$. We show
that $(G,\star,\bullet)$ is a double magma if and only if $G$
satisfies the commutator laws $[x,y;x,z]=1$ and $[w,x;y,z]^{2}=1$.
We note that the first law defines the class of 3metabelian
groups. If both these laws hold in $G$, the double magma is proper
if and only if there exist $x_0,y_0 \in G$ for which $[x_0,y_0]^2
\not= 1$. This double magma is a double semigroup if and only
if $G$ is nilpotent of class two. We construct a specific example
of a proper double semigroup based on the dihedral group of order
16. In addition we comment on a similar construction for rings
using Lie commutators.
Keywords:double magma, double semigroups, 3metabelian Categories:20E10, 20M99 

3. CMB Online first
 Laterveer, Robert

A brief note concerning hard Lefschetz for Chow groups
We formulate a conjectural hard Lefschetz property
for Chow groups, and prove this in some special cases: roughly
speaking, for varieties with finitedimensional motive, and
for varieties whose selfproduct has vanishing middledimensional
Griffiths group. An appendix includes related statements that
follow from results of Vial.
Keywords:algebraic cycles, Chow groups, finitedimensional motives Categories:14C15, 14C25, 14C30 

4. CMB 2015 (vol 58 pp. 241)
 Botelho, Fernanda

Isometries and Hermitian Operators on Zygmund Spaces
In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.
Keywords:Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of oneparameter groups of surjective isometries Categories:46E15, 47B15, 47B38 

5. CMB 2014 (vol 58 pp. 182)
6. CMB 2014 (vol 58 pp. 3)
7. CMB 2014 (vol 58 pp. 69)
 Fulp, Ronald Owen

Correction to "Infinite Dimensional DeWitt Supergroups and Their Bodies"
The Theorem below is a correction to Theorem
3.5 in the article
entitled " Infinite Dimensional DeWitt Supergroups and Their
Bodies" published
in Canad. Math. Bull. Vol. 57 (2) 2014 pp. 283288. Only part
(iii) of that Theorem
requires correction. The proof of Theorem 3.5 in the original
article failed to separate
the proof of (ii) from the proof of (iii). The proof of (ii)
is complete once it is established
that $ad_a$ is quasinilpotent for each $a$ since it immediately
follows that $K$
is quasinilpotent. The proof of (iii) is not complete
in the original article. The revision appears as the proof of
(iii) of the revised Theorem below.
Keywords:super groups, body of super groups, Banach Lie groups Categories:58B25, 17B65, 81R10, 57P99 

8. CMB 2014 (vol 57 pp. 708)
 Brannan, Michael

Strong Asymptotic Freeness for Free Orthogonal Quantum Groups
It is known that the normalized standard generators of the free
orthogonal quantum group $O_N^+$ converge in distribution to a free
semicircular system as $N \to \infty$. In this note, we
substantially improve this convergence result by proving that, in
addition to distributional convergence, the operator norm of any
noncommutative polynomial in the normalized standard generators of
$O_N^+$ converges as $N \to \infty$ to the operator norm of the
corresponding noncommutative polynomial in a standard free
semicircular system. Analogous strong convergence results are obtained
for the generators of free unitary quantum groups. As applications of
these results, we obtain a matrixcoefficient version of our strong
convergence theorem, and we recover a well known $L^2$$L^\infty$ norm
equivalence for noncommutative polynomials in free semicircular
systems.
Keywords:quantum groups, free probability, asymptotic free independence, strong convergence, property of rapid decay Categories:46L54, 20G42, 46L65 

9. CMB 2014 (vol 57 pp. 648)
 Tang, Juping; Miao, Long

On the ${\mathcal F}{\Phi}$Hypercentre of Finite Groups
Let $G$ be a finite group, $\mathcal F$ a class of groups.
Then $Z_{{\mathcal F}{\Phi}}(G)$ is the ${\mathcal F}{\Phi}$hypercentre
of $G$ which is the product of all normal subgroups of $G$ whose
nonFrattini $G$chief factors are $\mathcal F$central in $G$. A
subgroup $H$ is called $\mathcal M$supplemented in a finite group
$G$, if there exists a subgroup $B$ of $G$ such that $G=HB$ and
$H_1B$ is a proper subgroup of $G$ for any maximal subgroup $H_1$
of $H$. The main purpose of this paper is to prove: Let $E$ be a
normal subgroup of a group $G$. Suppose that every noncyclic
Sylow
subgroup $P$ of $F^{*}(E)$ has a subgroup $D$ such that
$1\lt D\lt P$ and every subgroup $H$ of $P$ with order $H=D$
is
$\mathcal M$supplemented in $G$, then $E\leq Z_{{\mathcal
U}{\Phi}}(G)$.
Keywords:${\mathcal F}{\Phi}$hypercentre, Sylow subgroups, $\mathcal M$supplemented subgroups, formation Categories:20D10, 20D20 

10. CMB 2014 (vol 57 pp. 511)
 Gonçalves, Daniel

Simplicity of Partial Skew Group Rings of Abelian Groups
Let $A$ be a ring with local units, $E$ a set of local units for $A$,
$G$ an abelian group and $\alpha$ a partial action of $G$ by ideals of
$A$ that contain local units.
We show that $A\star_{\alpha} G$ is simple if and only if $A$ is
$G$simple and the center of the corner $e\delta_0 (A\star_{\alpha} G)
e \delta_0$ is a field for all $e\in E$. We apply the result to
characterize simplicity of partial skew group rings in two cases,
namely for partial skew group rings arising from partial actions by
clopen subsets of a compact set and partial actions on the set level.
Keywords:partial skew group rings, simple rings, partial actions, abelian groups Categories:16S35, 37B05 

11. CMB 2014 (vol 57 pp. 277)
 Elkholy, A. M.; ElLatif, M. H. Abd

On Mutually $m$permutable Product of Smooth Groups
Let $G$ be a
finite group and $H$, $K$ two subgroups of G. A group $G$ is said to
be a mutually mpermutable product of $H$ and $K$ if $G=HK$ and
every maximal subgroup of $H$ permutes with $K$ and every maximal
subgroup of $K$ permutes with $H$. In this paper, we investigate the
structure of a finite group which is a mutually mpermutable product
of two subgroups under the assumption that its maximal subgroups are
totally smooth.
Keywords:permutable subgroups, $m$permutable, smooth groups, subgroup lattices Categories:20D10, 20D20, 20E15, 20F16 

12. CMB 2013 (vol 57 pp. 245)
 Brodskiy, N.; Dydak, J.; Lang, U.

AssouadNagata Dimension of Wreath Products of Groups
Consider the wreath product $H\wr G$, where $H\ne 1$ is finite and $G$ is finitely generated.
We show that the AssouadNagata dimension $\dim_{AN}(H\wr G)$ of $H\wr G$
depends on the growth of $G$ as follows:
\par If the growth of $G$ is not bounded by a linear function, then $\dim_{AN}(H\wr G)=\infty$,
otherwise $\dim_{AN}(H\wr G)=\dim_{AN}(G)\leq 1$.
Keywords:AssouadNagata dimension, asymptotic dimension, wreath product, growth of groups Categories:54F45, 55M10, 54C65 

13. CMB 2013 (vol 57 pp. 449)
 Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim

ZLamenability Constants of Finite Groups with Two Character Degrees
We calculate the exact amenability constant of the centre of
$\ell^1(G)$ when $G$ is one of the following classes of finite group:
dihedral; extraspecial; or Frobenius with abelian complement and
kernel. This is done using a formula which applies to all finite
groups with two character degrees. In passing, we answer in the
negative a question raised in work of the third author with Azimifard
and Spronk (J. Funct. Anal. 2009).
Keywords:center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups Categories:43A20, 20C15 

14. CMB 2013 (vol 57 pp. 125)
 Mlaiki, Nabil M.

Camina Triples
In this paper, we study Camina triples. Camina triples are a
generalization of Camina pairs. Camina pairs were first introduced
in 1978 by A .R. Camina.
Camina's work
was inspired by the study of Frobenius groups. We
show that if $(G,N,M)$ is a Camina triple, then either $G/N$ is a
$p$group, or $M$ is abelian, or $M$ has a nontrivial nilpotent or
Frobenius quotient.
Keywords:Camina triples, Camina pairs, nilpotent groups, vanishing off subgroup, irreducible characters, solvable groups Category:20D15 

15. CMB 2013 (vol 57 pp. 335)
 Karassev, A.; Todorov, V.; Valov, V.

Alexandroff Manifolds and Homogeneous Continua
ny homogeneous,
metric $ANR$continuum is a $V^n_G$continuum provided $\dim_GX=n\geq
1$ and $\check{H}^n(X;G)\neq 0$, where $G$ is a principal ideal
domain.
This implies that any homogeneous $n$dimensional metric $ANR$continuum is a $V^n$continuum in the sense of Alexandroff.
We also prove that any finitedimensional homogeneous metric continuum
$X$, satisfying $\check{H}^n(X;G)\neq 0$ for some group $G$ and $n\geq
1$, cannot be separated by
a compactum $K$ with $\check{H}^{n1}(K;G)=0$ and $\dim_G K\leq
n1$. This provides a partial answer to a question of
KallipolitiPapasoglu
whether any twodimensional homogeneous Peano continuum cannot be separated by arcs.
Keywords:Cantor manifold, cohomological dimension, cohomology groups, homogeneous compactum, separator, $V^n$continuum Categories:54F45, 54F15 

16. CMB 2013 (vol 57 pp. 546)
 Kalantar, Mehrdad

Compact Operators in Regular LCQ Groups
We show that a regular locally compact quantum group $\mathbb{G}$ is discrete
if and only if $\mathcal{L}^{\infty}(\mathbb{G})$ contains nonzero compact operators on
$\mathcal{L}^{2}(\mathbb{G})$.
As a corollary we classify all discrete quantum groups among
regular locally compact quantum groups $\mathbb{G}$ where
$\mathcal{L}^{1}(\mathbb{G})$ has the RadonNikodym property.
Keywords:locally compact quantum groups, regularity, compact operators Category:46L89 

17. CMB 2012 (vol 57 pp. 326)
 Ivanov, S. V.; Mikhailov, Roman

On Zerodivisors in Group Rings of Groups with Torsion
Nontrivial pairs of zerodivisors in group rings are
introduced and discussed. A problem on the existence of nontrivial
pairs of zerodivisors in group rings of free Burnside groups of odd
exponent $n \gg 1$ is solved in the affirmative. Nontrivial pairs of
zerodivisors are also found in group rings of free products of groups
with torsion.
Keywords:Burnside groups, free products of groups, group rings, zerodivisors Categories:20C07, 20E06, 20F05, , 20F50 

18. CMB 2012 (vol 57 pp. 289)
 Ghasemi, Mehdi; Marshall, Murray; Wagner, Sven

Closure of the Cone of Sums of $2d$powers in Certain Weighted $\ell_1$seminorm Topologies
In a paper from 1976, Berg, Christensen and Ressel prove that the
closure of the cone of sums of squares $\sum
\mathbb{R}[\underline{X}]^2$ in the polynomial ring
$\mathbb{R}[\underline{X}] := \mathbb{R}[X_1,\dots,X_n]$ in the
topology induced by the $\ell_1$norm is equal to
$\operatorname{Pos}([1,1]^n)$, the cone consisting of all polynomials
which are nonnegative on the hypercube $[1,1]^n$. The result is
deduced as a corollary of a general result, established in the same
paper, which is valid for any commutative semigroup.
In later work, Berg and Maserick and Berg, Christensen and Ressel
establish an even more general result, for a commutative semigroup
with involution, for the closure of the cone of sums of squares of
symmetric elements in the weighted $\ell_1$seminorm topology
associated to an absolute value.
In the present paper we give a new proof of these results which is
based on Jacobi's representation theorem from 2001. At the same time,
we use Jacobi's representation theorem to extend these results from
sums of squares to sums of $2d$powers, proving, in particular, that
for any integer $d\ge 1$, the closure of the cone of sums of
$2d$powers $\sum \mathbb{R}[\underline{X}]^{2d}$ in
$\mathbb{R}[\underline{X}]$ in the topology induced by the
$\ell_1$norm is equal to $\operatorname{Pos}([1,1]^n)$.
Keywords:positive definite, moments, sums of squares, involutive semigroups Categories:43A35, 44A60, 13J25 

19. CMB 2012 (vol 56 pp. 570)
 Hoang, Giabao; Ressler, Wendell

Conjugacy Classes and Binary Quadratic Forms for the Hecke Groups
In this paper we give a lower bound
with respect to block length
for the trace of nonelliptic conjugacy classes
of the Hecke groups.
One consequence of our bound
is that there are finitely many
conjugacy classes of a given trace in any Hecke group.
We show that another consequence of our bound
is that
class numbers are finite for
related hyperbolic \( \mathbb{Z}[\lambda] \)binary quadratic forms.
We give canonical class representatives
and calculate class numbers
for some classes of hyperbolic \( \mathbb{Z}[\lambda] \)binary quadratic forms.
Keywords:Hecke groups, conjugacy class, quadratic forms Categories:11F06, 11E16, 11A55 

20. CMB 2012 (vol 57 pp. 132)
 Mubeena, T.; Sankaran, P.

Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups
Given a group automorphism $\phi:\Gamma\longrightarrow \Gamma$, one has
an action of $\Gamma$ on itself by $\phi$twisted conjugacy, namely, $g.x=gx\phi(g^{1})$.
The orbits of this action are called $\phi$twisted conjugacy classes. One says
that $\Gamma$ has the $R_\infty$property if there are infinitely many $\phi$twisted conjugacy
classes for every automorphism $\phi$ of $\Gamma$. In this paper we
show that $\operatorname{SL}(n,\mathbb{Z})$ and its
congruence subgroups have the $R_\infty$property. Further we show that
any (countable) abelian extension of $\Gamma$ has the $R_\infty$property where $\Gamma$ is a torsion
free nonelementary hyperbolic group, or $\operatorname{SL}(n,\mathbb{Z}),
\operatorname{Sp}(2n,\mathbb{Z})$ or a principal congruence
subgroup of $\operatorname{SL}(n,\mathbb{Z})$ or the fundamental group of a complete Riemannian
manifold of constant negative curvature.
Keywords:twisted conjugacy classes, hyperbolic groups, lattices in Lie groups Category:20E45 

21. CMB 2012 (vol 56 pp. 630)
 Sundar, S.

Inverse Semigroups and Sheu's Groupoid for the Odd Dimensional Quantum Spheres
In this paper, we give a different proof of the fact that the odd dimensional
quantum spheres are groupoid $C^{*}$algebras. We show that the $C^{*}$algebra
$C(S_{q}^{2\ell+1})$ is generated by an inverse semigroup $T$ of partial
isometries. We show that the groupoid $\mathcal{G}_{tight}$ associated with the
inverse semigroup $T$ by Exel is exactly the same as the groupoid
considered by Sheu.
Keywords:inverse semigroups, groupoids, odd dimensional quantum spheres Categories:46L99, 20M18 

22. CMB 2011 (vol 56 pp. 229)
 Arvanitidis, Athanasios G.; Siskakis, Aristomenis G.

CesÃ ro Operators on the Hardy Spaces of the HalfPlane
In this article we study the CesÃ ro
operator
$$
\mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta,
$$
and its companion operator $\mathcal{T}$ on Hardy spaces of the
upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as
resolvents for appropriate semigroups of composition operators and we
find the norm and the spectrum in each case. The relation of
$\mathcal{C}$ and $\mathcal{T}$ with the corresponding Ces\`{a}ro
operators on Lebesgue spaces $L^p(\mathbb R)$ of the boundary line is also
discussed.
Keywords:CesÃ ro operators, Hardy spaces, semigroups, composition operators Categories:47B38, 30H10, 47D03 

23. CMB 2011 (vol 56 pp. 366)
 Kyritsi, Sophia Th.; Papageorgiou, Nikolaos S.

Multiple Solutions for Nonlinear Periodic Problems
We consider a nonlinear periodic problem driven by a
nonlinear nonhomogeneous differential operator and a
CarathÃ©odory reaction term $f(t,x)$ that exhibits a
$(p1)$superlinear growth in $x \in \mathbb{R}$
near $\pm\infty$ and near zero.
A special case of the differential operator is the scalar
$p$Laplacian. Using a combination of variational methods based on
the critical point theory with Morse theory (critical groups), we
show that the problem has three nontrivial solutions, two of which
have constant sign (one positive, the other negative).
Keywords:$C$condition, mountain pass theorem, critical groups, strong deformation retract, contractible space, homotopy invariance Categories:34B15, 34B18, 34C25, 58E05 

24. CMB 2011 (vol 55 pp. 870)
 Wang, Hui; Deng, Shaoqiang

Left Invariant EinsteinRanders Metrics on Compact Lie Groups
In this paper we study left invariant EinsteinRanders metrics on compact Lie
groups. First, we give a method to construct left invariant nonRiemannian EinsteinRanders metrics
on a compact Lie group, using the Zermelo navigation data.
Then we prove that this gives a complete classification of left invariant EinsteinRanders metrics on compact simple
Lie groups with the underlying Riemannian metric naturally reductive.
Further, we completely determine the identity component of the group of
isometries for this type of metrics on simple groups. Finally, we study some
geometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvature
of such metrics.
Keywords:EinsteinRanders metric, compact Lie groups, geodesic, flag curvature Categories:17B20, 22E46, 53C12 

25. CMB 2011 (vol 56 pp. 218)
 Yang, Dilian

Functional Equations and Fourier Analysis
By exploring the relations among functional equations, harmonic analysis and representation theory,
we give a unified and very accessible approach to solve three important functional equations 
the d'Alembert equation, the Wilson equation, and the d'Alembert long equation 
on compact groups.
Keywords:functional equations, Fourier analysis, representation of compact groups Categories:39B52, 22C05, 43A30 
