The Baer-invariant of a semidirect product

Generalized Baer-Invariant of a Pair of Groups and the Direct Limit

In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...

Generalized Baer-Invariant of a Pair of Groups and Marginal Extension

In this paper, we give connection between the order of the generalized Baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. Moreover, we give a necessary and sufficient condition in which the generalized Baer-invariant of a pair of groups can be embedded into the generalized Baer-invariant of pair of its factor groups.

Invariant random subgroups of semidirect products

We study invariant random subgroups (IRSs) of semidirect products G = AoΓ. In particular, we characterize all IRSs of parabolic subgroups of SLd(R), and show that all ergodic IRSs of Rdo SLd(R) are either of the form RdoK for some IRS of SLd(R), or are induced from IRSs of Λo SL(Λ), where Λ < Rd is a lattice.

The Semidirect Product of an Inverse Semigroup and a Group

Semidirect product decomposition of Coxeter groups

Let (W,S) be a Coxeter system, let S = I ∪ J be a partition of S such that no element of I is conjugate to an element of J , let J̃ be the set of WI -conjugates of elements of J and let W̃ be the subgroup of W generated by J̃ . We show that W = W̃ ⋊WI and that J̃ is the canonical set of Coxeter generators of the reflection subgroup W̃ of W . We also provide algebraic and geometric conditions for an e...