1. CMB 2011 (vol 56 pp. 344)
 Goodaire, Edgar G.; Milies, César Polcino

Involutions and Anticommutativity in Group Rings
Let $g\mapsto g^*$ denote an involution on a
group $G$. For any (commutative, associative) ring
$R$ (with $1$), $*$ extends linearly to an involution
of the group ring $RG$. An element $\alpha\in RG$
is symmetric if $\alpha^*=\alpha$ and
skewsymmetric if $\alpha^*=\alpha$.
The skewsymmetric elements are closed under
the Lie bracket, $[\alpha,\beta]=\alpha\beta\beta\alpha$.
In this paper, we investigate when this set is also closed
under the ring product in $RG$.
The symmetric elements are closed under the Jordan
product, $\alpha\circ\beta=\alpha\beta+\beta\alpha$.
Here, we determine when this product is trivial.
These two problems
are analogues of problems about the skewsymmetric and
symmetric elements in group rings that have received a
lot of attention.
Categories:16W10, 16S34 

2. CMB 2010 (vol 54 pp. 237)
 Creedon, Leo; Gildea, Joe

The Structure of the Unit Group of the Group Algebra ${\mathbb{F}}_{2^k}D_{8}$
Let $RG$ denote the group ring of the group $G$ over
the ring $R$. Using an isomorphism between $RG$ and a
certain ring of $n \times n$ matrices in conjunction with other
techniques, the structure of the unit group of the group algebra
of the dihedral group of order $8$ over any
finite field of chracteristic $2$ is determined in
terms of split extensions of cyclic groups.
Categories:16U60, 16S34, 20C05, 15A33 

3. CMB 2008 (vol 51 pp. 291)
 Spinelli, Ernesto

Group Algebras with Minimal Strong Lie Derived Length
Let $KG$ be a noncommutative strongly Lie solvable group algebra of a
group $G$ over a field $K$ of positive characteristic $p$. In this
note we state necessary and sufficient conditions so that the
strong Lie derived length of $KG$ assumes its minimal value, namely
$\lceil \log_{2}(p+1)\rceil $.
Keywords:group algebras, strong Lie derived length Categories:16S34, 17B30 

4. CMB 2005 (vol 48 pp. 80)
 Herman, Allen; Li, Yuanlin; Parmenter, M. M.

Trivial Units for Group Rings with $G$adapted Coefficient Rings
For each finite group $G$ for which the integral group ring
$\mathbb{Z}G$ has only trivial units, we give ringtheoretic
conditions for a commutative ring $R$ under which the group ring
$RG$ has nontrivial units. Several examples of rings satisfying
the conditions and rings not satisfying the conditions are given.
In addition, we extend a wellknown result for fields by showing
that if $R$ is a ring of finite characteristic and $RG$ has only
trivial units, then $G$ has order at most 3.
Categories:16S34, 16U60, 20C05 

5. CMB 2003 (vol 46 pp. 14)
6. CMB 2001 (vol 44 pp. 27)
7. CMB 2000 (vol 43 pp. 100)
8. CMB 2000 (vol 43 pp. 60)
 Farkas, Daniel R.; Linnell, Peter A.

Trivial Units in Group Rings
Let $G$ be an arbitrary group and let $U$ be a subgroup of the
normalized units in $\mathbb{Z}G$. We show that if $U$ contains $G$
as a subgroup of finite index, then $U = G$. This result can be used
to give an alternative proof of a recent result of Marciniak and
Sehgal on units in the integral group ring of a crystallographic group.
Keywords:units, trace, finite conjugate subgroup Categories:16S34, 16U60 

9. CMB 1998 (vol 41 pp. 481)
10. CMB 1998 (vol 41 pp. 109)
 Tahara, KenIchi; Vermani, L. R.; Razdan, Atul

On generalized third dimension subgroups
Let $G$ be any group, and $H$ be a normal subgroup of $G$. Then M.~Hartl
identified the subgroup $G \cap(1+\triangle^3(G)+\triangle(G)\triangle(H))$
of $G$. In this note we give an independent proof of the result of Hartl,
and we identify two subgroups
$G\cap(1+\triangle(H)\triangle(G)\triangle(H)+\triangle([H,G])\triangle(H))$,
$G\cap(1+\triangle^2(G)\triangle(H)+\triangle(K)\triangle(H))$ of $G$ for
some subgroup $K$ of $G$ containing $[H,G]$.
Categories:20C07, 16S34 
