Title : ( On Baer invariants of pairs of groups )
Authors: Behrooz Mashayekhy Fard , Bibi Hanieh Mirebrahimi Paziquee , Zohreh Vasagh ,
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Abstract
In this paper, we use the theory of simplicial groups to develop the Schur multiplier of a pair of groups $(G,N)$ to the Baer invariant of it, $\mathcal{V}M(G,N)$, with respect to an arbitrary variety $\mathcal{V}$. Moreover, we present among other things some behaviors of Baer invariants of a pair of groups with respect to the free product and the direct limit. Finally we prove that the nilpotent multiplier of a pair of groups does commute with the free product of finite groups of mutually coprime orders.
Keywords
, Baer invariant, Pair of groups, Simplicial groups.
@article{paperid:1048190,
author = {Mashayekhy Fard, Behrooz and Mirebrahimi Paziquee, Bibi Hanieh and Vasagh, Zohreh},
title = {On Baer invariants of pairs of groups},
journal = {Georgian Mathematical Journal},
year = {2018},
volume = {25},
number = {3},
month = {September},
issn = {1072-947X},
pages = {461--473},
numpages = {12},
keywords = {Baer invariant; Pair of groups; Simplicial groups.},
}
%0 Journal Article
%T On Baer invariants of pairs of groups
%A Mashayekhy Fard, Behrooz
%A Mirebrahimi Paziquee, Bibi Hanieh
%A Vasagh, Zohreh
%J Georgian Mathematical Journal
%@ 1072-947X
%D 2018
