The ranks of central factor and commutator groups

Abstract

The Schur Theorem says that if $G$ is a group whose center $Z(G)$ has finite index $n$, then the order of the derived group $G^{\prime }$ is finite and bounded by a number depending only on $n$. In the present paper we show that if $G$ is a finite group such that $G/Z(G)$ has rank $r$, then the rank of $G^{\prime }$ is $r$-bounded. We also show that a similar result holds for a large class of infinite groups.

Cited by in corpus (1)

• On the rank of a verbal subgroup of a finite group