on the order of the schur multiplier of a pair of finite p-groups ii
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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 have characterized the structure of $(g,n)$ when $n$ has a complement in $g$ and $tleq 3$. this paper is devoted to classification of pairs $(g,n)$ when $n$ has a normal complement in $g$ and $t=4,5$.
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Journal title:
international journal of group theoryPublisher: university of isfahan
ISSN 2251-7650
volume 2
issue 3 2012
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