1. CMB 2014 (vol 57 pp. 884)
 Xu, Yong; Zhang, Xinjian

$m$embedded Subgroups and $p$nilpotency of Finite Groups
Let $A$ be a subgroup of a finite group $G$ and $\Sigma : G_0\leq
G_1\leq\cdots \leq G_n$ some subgroup series of $G$. Suppose that
for each pair $(K,H)$ such that $K$ is a maximal subgroup of $H$ and
$G_{i1}\leq K \lt H\leq G_i$, for some $i$, either $A\cap H = A\cap K$
or $AH = AK$. Then $A$ is said to be $\Sigma$embedded in $G$; $A$
is said to be $m$embedded in $G$ if $G$ has a subnormal subgroup
$T$ and a $\{1\leq G\}$embedded subgroup $C$ in $G$ such that $G =
AT$ and $T\cap A\leq C\leq A$. In this article, some sufficient
conditions for a finite group $G$ to be $p$nilpotent are given
whenever all subgroups with order $p^{k}$ of a Sylow $p$subgroup of
$G$ are $m$embedded for a given positive integer $k$.
Keywords:finite group, $p$nilpotent group, $m$embedded subgroup Categories:20D10, 20D15 

2. 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 

3. CMB 2001 (vol 44 pp. 266)
 Cencelj, M.; Dranishnikov, A. N.

Extension of Maps to Nilpotent Spaces
We show that every compactum has cohomological dimension $1$ with respect
to a finitely generated nilpotent group $G$ whenever it has cohomological
dimension $1$ with respect to the abelianization of $G$. This is applied
to the extension theory to obtain a cohomological dimension theory condition
for a finitedimensional compactum $X$ for extendability of every map from
a closed subset of $X$ into a nilpotent $\CW$complex $M$ with finitely
generated homotopy groups over all of $X$.
Keywords:cohomological dimension, extension of maps, nilpotent group, nilpotent space Categories:55M10, 55S36, 54C20, 54F45 

4. CMB 1999 (vol 42 pp. 335)
 Kim, Goansu; Tang, C. Y.

Cyclic Subgroup Separability of HNNExtensions with Cyclic Associated Subgroups
We derive a necessary and sufficient condition for HNNextensions
of cyclic subgroup separable groups with cyclic associated
subgroups to be cyclic subgroup separable. Applying this, we
explicitly characterize the residual finiteness and the cyclic
subgroup separability of HNNextensions of abelian groups with
cyclic associated subgroups. We also consider these residual
properties of HNNextensions of nilpotent groups with cyclic
associated subgroups.
Keywords:HNNextension, nilpotent groups, cyclic subgroup separable $(\pi_c)$, residually finite Categories:20E26, 20E06, 20F10 
