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The Coherence Number of 2-Groups

Published online by Cambridge University Press:  20 November 2018

James McCool
James McCool*
Affiliation:
Department of Mathemtics University of Toronto Toronto, M5S 1A1, Canada
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Abstract

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Let G be a finite group. A natural invariant c(G) of G has been defined by W.J. Ralph, as the order (possibly infinite) of a distinguished element of a certain abelian group associated to G. Ralph has shown that c(Zn) = 1 and c(Z2 ⴲ Z2) = 2. In the present paper we show that c(G) is finite whenever G is a dihedral group or a 2-group, and obtain upper bounds for c(G) in these cases.

Keywords

20D6020E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 503 - 508
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Lyndon, R. C. and Schupp, RE., Combinatorial Group Theory, Springer-Verlag, New York, 1977.Google Scholar
2. Ralph, W. J., The coherence number of a finite group, J. Algebra 126 (1989), 61–79.Google Scholar