On the Exponent of the Schur multiplier of a Pair of Finite p-Groups

الأصل · EN

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 (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 (N).