1. CMB Online first
 Motegi, Kimihiko; Teragaito, Masakazu

Generalized torsion elements and biorderability of 3manifold groups
It is known that a biorderable group has no generalized torsion
element,
but the converse does not hold in general.
We conjecture that the converse holds for the fundamental groups
of $3$manifolds,
and verify the conjecture for nonhyperbolic, geometric $3$manifolds.
We also confirm the conjecture for some infinite families of
closed hyperbolic $3$manifolds.
In the course of the proof,
we prove that each standard generator of the Fibonacci group
$F(2, m)$ ($m \gt 2$) is a generalized torsion element.
Keywords:generalized torsion element, biordering, 3manifold group Categories:57M25, 57M05, 06F15, 20F05 

2. 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 

3. CMB 2011 (vol 56 pp. 395)
 Oancea, D.

Coessential Abelianization Morphisms in the Category of Groups
An epimorphism $\phi\colon G\to H$ of groups, where $G$ has rank $n$, is called
coessential if every (ordered) generating $n$tuple of $H$ can be
lifted along $\phi$ to a generating $n$tuple for $G$. We discuss this
property in the context of the category of groups, and establish a criterion
for such a group $G$ to have the property that its abelianization
epimorphism $G\to G/[G,G]$, where $[G,G]$ is the commutator subgroup, is
coessential. We give an example of a family of 2generator groups whose
abelianization epimorphism is not coessential.
This family also provides counterexamples to the generalized AndrewsCurtis conjecture.
Keywords:coessential epimorphism, Nielsen transformations, AndrewCurtis transformations Categories:20F05, 20F99, 20J15 

4. CMB 2006 (vol 49 pp. 347)
 Ecker, Jürgen

Affine Completeness of Generalised Dihedral Groups
In this paper we study affine completeness of generalised dihedral
groups. We give a formula for the number of unary compatible
functions on these groups, and we characterise for every $k \in~\N$
the $k$affine complete generalised dihedral groups. We find that
the direct product of a $1$affine complete group with itself need not
be $1$affine complete. Finally, we give an example of a nonabelian
solvable affine complete group. For nilpotent groups we find a
strong necessary condition for $2$affine completeness.
Categories:08A40, 16Y30, 20F05 

5. CMB 2003 (vol 46 pp. 310)
6. CMB 2003 (vol 46 pp. 299)
7. CMB 1998 (vol 41 pp. 231)
 Worthington, R. L.

The growth series of compact hyperbolic Coxeter groups with 4 and 5 generators
The growth series of compact hyperbolic Coxeter groups with 4 and 5
generators are explicitly calculated. The assertions of J.~Cannon
and Ph.~Wagreich for the 4generated groups, that the poles of the
growth series lie
on the unit circle, with the exception of a single real reciprocal pair of
poles, are verified. We also verify that for the 5generated groups, this
phenomenon fails.
Categories:20F05, 20F55 
