Classification of finite p-groups by the size of their Schur multipliers

2017/06/07 by Niroomand, Peyman, Johari, Farangi
#20D15 (Primary) #20E34. 20F18 (Secondary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1706.02340

Abstract

Let d(G) be the minimum number of elements required to generated a group G. For a group G of order pⁿ with derived subgroup of order p^k and d(G) = d, we knew the order of the Schur multiplier of G is bounded by p^{(1)/(2)(d-1)(n-k+2)+1}. In the current paper, we find the structure of all p-groups that attains the mentioned bound. Moreover, we show that all of them are capable.

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