COMMUTING POWERS AND EXTERIOR DEGREE OF FINITE GROUPS

Title & Authors
COMMUTING POWERS AND EXTERIOR DEGREE OF FINITE GROUPS
Niroomand, Peyman; Rezaei, Rashid; Russo, Francesco G.;

Abstract
Recently, we have introduced a group invariant, which is related to the number of elements $\small{x}$ and $\small{y}$ of a finite group $\small{G}$ such that $\small{x{\wedge}y=1_{G{\wedge}G}}$ in the exterior square $\small{G{\wedge}G}$ of $\small{G}$. This number gives restrictions on the Schur multiplier of $\small{G}$ and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form $\small{h^m{\wedge}k}$ of $\small{H{\wedge}K}$ such that $\small{h^m{\wedge}k=1_{H{\wedge}K}}$, where $\small{m{\geq}1}$ and $\small{H}$ and $\small{K}$ are arbitrary subgroups of $\small{G}$.
Keywords
m-th relative exterior degree;commutativity degree;exterior product;Schur multiplier;homological algebra;
Language
English
Cited by
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2.
Probabilistic properties of the relative tensor degree of finite groups, Indagationes Mathematicae, 2016, 27, 1, 147
3.
The Influence of the Complete Nonexterior Square Graph on some Infinite Groups, Lithuanian Mathematical Journal, 2016, 56, 4, 492
4.
Problems of Connectivity between the Sylow Graph,the Prime Graph and the Non-Commuting Graph of a Group, Advances in Pure Mathematics, 2012, 02, 06, 391
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