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 $\exp (N)$.

arXiv comment11 pages

References in corpus (1)

• On a Conjecture of a Bound for the Exponent of the Schur Multiplier of a Finite $p$-Group