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arXiv · 1204.4641

The ranks of central factor and commutator groups

Leonid A. Kurdachenko·Pavel Shumyatsky
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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 $G'$ 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 $G'$ is $r$-bounded. We also show that a similar result holds for a large class of infinite groups.

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Leonid A. Kurdachenko, Pavel Shumyatsky. 2012-04-25. The ranks of central factor and commutator groups. https://doi.org/10.1017/s0305004112000412

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