Expand all Collapse all | Results 1 - 9 of 9 |
1. CMB Online first
On Finite Groups with Dismantlable Subgroup Lattices In this note we study the finite groups whose subgroup
lattices are dismantlable.
Keywords:finite groups, subgroup lattices, dismantlable lattices, planar lattices, crowns Categories:20D30, 20D60, 20E15 |
2. CMB 2014 (vol 57 pp. 277)
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 m-permutable 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 m-permutable 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 |
3. CMB 2012 (vol 57 pp. 132)
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 non-elementary 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 |
4. CMB 2011 (vol 56 pp. 659)
Asymptotics and Uniqueness of Travelling Waves for Non-Monotone Delayed Systems on 2D Lattices We establish asymptotics and uniqueness (up
to translation) of travelling waves for delayed 2D lattice equations
with non-monotone birth functions. First, with the help of
Ikehara's Theorem, the a priori asymptotic behavior of
travelling wave is exactly derived. Then, based on the obtained
asymptotic behavior, the uniqueness of the traveling waves is
proved. These results complement earlier results in the literature.
Keywords:2D lattice systems, traveling waves, asymptotic behavior, uniqueness, nonmonotone nonlinearity Category:35K57 |
5. CMB 2011 (vol 54 pp. 645)
An Extension of Craig's Family of Lattices Let $p$ be a prime, and let $\zeta_p$ be a primitive $p$-th root of
unity. The lattices in Craig's family are $(p-1)$-dimensional and
are geometrical representations of the integral $\mathbb
Z[\zeta_p]$-ideals $\langle 1-\zeta_p \rangle^i$, where $i$ is a
positive integer. This lattice construction technique is a powerful
one. Indeed, in dimensions $p-1$ where $149 \leq p \leq 3001$,
Craig's lattices are the densest packings known. Motivated by this,
we construct $(p-1)(q-1)$-dimensional lattices from the integral
$\mathbb Z[\zeta _{pq}]$-ideals $\langle 1-\zeta_p \rangle^i \langle
1-\zeta_q \rangle^j$, where $p$ and $q$ are distinct primes and $i$
and $j$ are positive integers. In terms of sphere-packing density,
the new lattices and those in Craig's family have the same
asymptotic behavior. In conclusion, Craig's family is greatly
extended while preserving its sphere-packing properties.
Keywords:geometry of numbers, lattice packing, Craig's lattices, quadratic forms, cyclotomic fields Categories:11H31, 11H55, 11H50, 11R18, 11R04 |
6. CMB 2011 (vol 54 pp. 277)
Maximal Sublattices of Finite Distributive Lattices. III: A Conjecture from the 1984 Banff Conference on Graphs and Order |
Maximal Sublattices of Finite Distributive Lattices. III: A Conjecture from the 1984 Banff Conference on Graphs and Order Let $L$ be a finite distributive lattice. Let
$\operatorname{Sub}_0(L)$ be the lattice
$$
\{S\mid S\text{ is a sublattice of }L\}\cup\{\emptyset\}
$$
and let $\ell_*[\operatorname{Sub}_0(L)]$ be the length of the shortest maximal chain in $\operatorname{Sub}_0(L)$. It is proved that if $K$ and $L$ are non-trivial finite distributive lattices, then
$$
\ell_*[\operatorname{Sub}_0(K\times L)]=\ell_*[\operatorname{Sub}_0(K)]+\ell_*[\operatorname{Sub}_0(L)].
$$
A conjecture from the 1984 Banff Conference on Graphs and Order is thus proved.
Keywords:(distributive) lattice, maximal sublattice, (partially) ordered set Categories:06D05, 06D50, 06A07 |
7. CMB 2008 (vol 51 pp. 15)
The Duality Problem for the Class of AM-Compact Operators on Banach Lattices We prove the converse of a
theorem of Zaanen about the duality problem of
positive AM-compact operators.
Keywords:AM-compact operator, order continuous norm, discrete vector lattice Categories:46A40, 46B40, 46B42 |
8. CMB 2004 (vol 47 pp. 191)
Congruence Class Sizes in Finite Sectionally Complemented Lattices The congruences of a finite sectionally complemented lattice $L$ are
not necessarily \emph{uniform} (any two congruence classes of a
congruence are of the same size). To measure how far a congruence
$\Theta$ of $L$ is from being uniform, we introduce $\Spec\Theta$, the
\emph{spectrum} of $\Theta$, the family of cardinalities of the
congruence classes of $\Theta$. A typical result of this paper
characterizes the spectrum $S = (m_j \mid j < n)$ of a nontrivial
congruence $\Theta$ with the following two properties:
\begin{enumerate}[$(S_2)$]
\item[$(S_1)$] $2 \leq n$ and $n \neq 3$.
\item[$(S_2)$] $2 \leq m_j$ and $m_j \neq 3$, for all $j Keywords:congruence lattice, congruence-preserving extension Categories:06B10, 06B15 |
9. CMB 2002 (vol 45 pp. 483)
Diffraction of Weighted Lattice Subsets A Dirac comb of point measures in Euclidean space with bounded
complex weights that is supported on a lattice $\varGamma$ inherits
certain general properties from the lattice structure. In
particular, its autocorrelation admits a factorization into a
continuous function and the uniform lattice Dirac comb, and its
diffraction measure is periodic, with the dual lattice
$\varGamma^*$ as lattice of periods. This statement remains true
in the setting of a locally compact Abelian group whose topology
has a countable base.
Keywords:diffraction, Dirac combs, lattice subsets, homometric sets Categories:52C07, 43A25, 52C23, 43A05 |