1. CMB Online first
 Akbari, Saieed; Miraftab, Babak; Nikandish, Reza

CoMaximal Graphs of Subgroups of Groups
Let $H$ be a group. The comaximal graph of subgroups
of $H$, denoted by $\Gamma(H)$, is a
graph whose vertices are nontrivial and proper subgroups of
$H$ and two distinct vertices $L$
and $K$ are adjacent in $\Gamma(H)$ if and only if $H=LK$. In
this paper, we study the connectivity, diameter, clique number
and vertex
chromatic number of $\Gamma(H)$. For instance, we show that
if $\Gamma(H)$ has no isolated vertex, then $\Gamma(H)$
is connected with diameter at most $3$. Also, we characterize
all finite groups whose comaximal graphs are connected.
Among other results, we show that if $H$ is a finitely generated
solvable group and $\Gamma(H)$ is connected and moreover the
degree of a maximal subgroup is finite, then $H$ is finite.
Furthermore, we show that the degree of each vertex in the
comaximal graph of a general linear group over an algebraically
closed field is zero or infinite.
Keywords:comaximal graphs of subgroups of groups, diameter, nilpotent group, solvable group Categories:05C25, 05E15, 20D10, 20D15 

2. CMB 2010 (vol 53 pp. 757)
 Woo, Alexander

Interval Pattern Avoidance for Arbitrary Root Systems
We extend the idea of interval pattern avoidance defined by Yong and
the author for $S_n$ to arbitrary Weyl groups using the definition of
pattern avoidance due to Billey and Braden, and Billey and Postnikov.
We show that, as previously shown by Yong and the
author for $\operatorname{GL}_n$, interval pattern avoidance is a universal tool for
characterizing which Schubert varieties have certain local properties,
and where these local properties hold.
Categories:14M15, 05E15 

3. CMB 2007 (vol 50 pp. 535)
 Hohlweg, Christophe

Generalized Descent Algebras
If $A$ is a subset of the set of reflections of a finite Coxeter
group $W$, we define a sub$\ZM$module $\DC_A(W)$ of the group
algebra $\ZM W$. We discuss cases where this submodule is a
subalgebra. This family of subalgebras includes strictly the
Solomon descent algebra, the group algebra and, if $W$ is of type
$B$, the MantaciReutenauer algebra.
Keywords:Coxeter group, Solomon descent algebra, descent set Categories:20F55, 05E15 

4. CMB 2002 (vol 45 pp. 537)