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Infinite groups arising from partial presentations of finite groups

Published online by Cambridge University Press:  01 November 1999

GEORGE M. BERGMAN
GEORGE M. BERGMAN
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA; e-mail: gbergman@math.berkeley.edu
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Abstract

If G is a finite group, X a generating set for G and R some set of relations holding among these generators (but not in general a full set of relations presenting G), we establish sufficient conditions for the group G* = 〈X/R〉 to be infinite and give a lower bound for the rank of the abelianization of the kernel of the natural map G*→G. Related results in the literature and possible directions for generalization are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 3 , November 1999 , pp. 425 - 439
Copyright
© The Cambridge Philosophical Society 1999

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Footnotes

Part of this work was done while the author was partly supported by NSF contract DMS 93-03379.