On the Order of the Schur Multiplier of a Pair of Finite p-Groups II

Let \(G\) be a finite \(p\)-group and \(N\) be a normal subgroup of \(G\), with \(|N|=p^n\) and \(|G/N|=p^m\). A result of Ellis (1998) shows that the order of the Schur multiplier of such a pair \((G,N)\) of finite \(p\)-groups is bounded by \( p^{\frac{1}{2}n(2m+n-1)}\) and hence it is equal to \(...

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Bibliographic Details
Published in:arXiv.org 2017-02
Main Authors: Mohammadzadeh, Fahimeh, Hokmabadi, Azam, Mashayekhy, Behrooz
Format: Article
Language:English
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Subgroups
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Summary:Let \(G\) be a finite \(p\)-group and \(N\) be a normal subgroup of \(G\), with \(|N|=p^n\) and \(|G/N|=p^m\). A result of Ellis (1998) shows that the order of the Schur multiplier of such a pair \((G,N)\) of finite \(p\)-groups is bounded by \( p^{\frac{1}{2}n(2m+n-1)}\) and hence it is equal to \( p^{\frac{1}{2}n(2m+n-1)-t}\), for some non-negative integer \(t\). Recently the authors characterized the structure of \((G,N)\) when \(N\) has a complement in \(G\) and \(t\leq 3\). This paper is devoted to classify the structure of \((G,N)\) when \(N\) has a normal complement in \(G\) and \(t=4,5\).
ISSN:2331-8422