ON THE EXPONENT OF THE SCHUR MULTIPLIER OF A PAIR OF FINITE p-GROUPS

Abstract

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).

On the Exponent of the Schur Multiplier

“…In [15], the authors prove the conjecture for powerful groups. The authors of [18] prove that if N is powerfully embedded in G, then the exp(M(G, N)) | exp(N). In the theorem below, we generalize both these results.…”