A note on the Schur multiplier of groups of prime power order

Abstract

By a well-known result of Green (Proc R Soc A 237:574–581, 1956) and the formal definition of Ellis and Wiegold (Bull Austral Math Soc 60:191–196, 1999), there is an integer t, say corank(G), such that \({|\mathcal{M}(G)| = p^{\frac{1}{2}n(n-1)-t}}\). In Niroomand (J Algebra 322:4479–4482, 2009), the author showed for a non-abelian group G, corank(G) ≥ logp(|G|)−2 and classified the structure of all non-abelian p-groups of corank logp(|G|)−2. In the present paper, we are interesting to characterize the structure of all p-groups of corank logp(|G|)−1.