ﻻ يوجد ملخص باللغة العربية
Malnormal subgroups occur in various contexts. We review a large number of examples, and we compare the situation in this generality to that of finite Frobenius groups of permutations. In a companion paper [HaWe], we analyse when peripheral subgroups of knot groups and 3-manifold groups are malnormal.
A finite group $P$ is said to be emph{primary} if $|P|=p^{a}$ for some prime $p$. We say a primary subgroup $P$ of a finite group $G$ satisfies the emph{Frobenius normalizer condition} in $G$ if $N_{G}(P)/C_{G}(P)$ is a $p$-group provided $P$ is $p$-
We prove that a uniform pro-p group with no nonabelian free subgroups has a normal series with torsion-free abelian factors. We discuss this in relation to unique product groups. We also consider generalizations of Hantzsche-Wendt groups.
We prove that all invariant random subgroups of the lamplighter group $L$ are co-sofic. It follows that $L$ is permutation stable, providing an example of an infinitely presented such a group. Our proof applies more generally to all permutational wre
Let $w$ be a multilinear commutator word. In the present paper we describe recent results that show that if $G$ is a profinite group in which all $w$-values are contained in a union of finitely (or in some cases countably) many subgroups with a presc
In 1933 B.~H.~Neumann constructed uncountably many subgroups of ${rm SL}_2(mathbb Z)$ which act regularly on the primitive elements of $mathbb Z^2$. As pointed out by Magnus, their images in the modular group ${rm PSL}_2(mathbb Z)cong C_3*C_2$ are ma