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Spotting infinite groups

Published online by Cambridge University Press:  01 January 1999

DANIEL ALLCOCK
DANIEL ALLCOCK
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112; e-mail: [email protected]
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Abstract

We generalize a theorem of R. Thomas, which sometimes allows one to tell by inspection that a finitely presented group G is infinite. Groups to which his theorem applies have presentations with not too many more relators than generators, with at least some of the relators being proper powers. Our generalization provides lower bounds for the ranks of the abelianizations of certain normal subgroups of G in terms of their indices. We derive Thomas's theorem as a special case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 125 , Issue 1 , January 1999 , pp. 39 - 42
Copyright
Cambridge Philosophical Society 1999

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