On the exponent of the schur multiplier of a pair of finite p-groups

摘要

In this paper, we find an upper bound for the exponent of the Schur multiplier of a pair (G, N) of finite p-groups, when N admits a complement in G. As a consequence, we show that the exponent of the Schur multiplier of a pair (G, N) divides exp(N) if (G, N) is a pair of finite p-groups of class at most p - 1. We also prove that if N is powerfully embedded in G, then the exponent of the Schur multiplier of a pair (G, N) divides exp(N).