A further investigation on the order of the Schur multiplier of $p$- groups

Peyman Niroomand, Farangi Johari

Published 2017-06-07Version 1

For a $p$-group $G$ of order $ p^n$ with the derived subgroup of order $ p^k $ if $ d=d(G), $ the minimal number of elements required to generate $ G, $ then the order of Schur multiplier of $G$ is bounded by $ p^{\frac{1}{2}(d-1)(n-k+2)+1}. $ In the current manuscript, we find the structure of all $p$-groups that attains the mentioned bound. Moreover, we show that all of them are capable.