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The ranks of central factor and commutator groups

Published online by Cambridge University Press:  14 August 2012

LEONID A. KURDACHENKO  and
PAVEL SHUMYATSKY
LEONID A. KURDACHENKO
Affiliation:
Department of Algebra, National University of Dnepropetrovsk 72 Gagarin Av., Dnepropetrovsk, Ukraine49010. e-mail: [email protected]
PAVEL SHUMYATSKY
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900Brazil. e-mail: [email protected]
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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 this 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 1 , January 2013 , pp. 63 - 69
Copyright
Copyright © Cambridge Philosophical Society 2012

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