Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771790 | Journal of Algebra | 2017 | 8 Pages |
Abstract
Let G be a non-abelian p-group of order pn and M(G) denote the Schur multiplier of G. Niroomand proved that |M(G)|â¤p12(n+kâ2)(nâkâ1)+1 for non-abelian p-groups G of order pn with derived subgroup of order pk. Recently Rai classified p-groups G of nilpotency class 2 for which |M(G)| attains this bound. In this article we show that there is no finite p-group G of nilpotency class câ¥3 for pâ 3 such that |M(G)| attains this bound. Hence |M(G)|â¤p12(n+kâ2)(nâkâ1) for p-groups G of class câ¥3 where pâ 3. We also construct a p-group G for p=3 such that |M(G)| attains the Niroomand's bound.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Sumana Hatui,