On Baer invariants of pairs of groups

Behrooz Mashayekhy; Hanieh Mirebrahimi; Zohreh Vasagh

doi:10.1515/gmj-2016-0067

Article

On Baer invariants of pairs of groups

Behrooz Mashayekhy , Hanieh Mirebrahimi and Zohreh Vasagh

Published/Copyright: December 14, 2016

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From the journal Georgian Mathematical Journal Volume 25 Issue 3

Abstract

In this paper, we use the theory of simplicial groups to generalize the Schur multiplier of a pair of groups (G,N) to its Baer invariant, 𝒱⁢M⁢(G,N), with respect to an arbitrary variety 𝒱. Moreover, among other things we present 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

MSC 2010: 20E06; 20F18; 55U10

Acknowledgements

The authors would like to thank the referee for his/her thorough review and valuable suggestions on the improvement of the paper.

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Received: 2014-12-22

Accepted: 2015-05-14

Published Online: 2016-12-14

Published in Print: 2018-09-01

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https://doi.org/10.1515/gmj-2016-0067

Keywords for this article

Baer invariant; pair of groups; simplicial groups