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Cogrowth of groups and the Dedekind–Frobenius group determinant

Published online by Cambridge University Press:  01 March 1997

STEPHEN P. HUMPHRIES
STEPHEN P. HUMPHRIES
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602, U.S.A. email: steve@math.byu.edu
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Abstract

Let

formula here

be a presentation for the group G where F = 〈a1, …, an〉 is a free group. Put A = {a1, …, ana−11, …, a−1n} and call n the degree of the presentation. For g ∈ G, c ∈ A we let W(k, g, c) be the set of freely reduced words w ∈ F having length k, which end (on the right) in c and which represent the element g ∈ G. Let w(k, g, c) = |W(k, g, c)|. The function

formula here

will be called the cogrowth function for this presentation. Let

formula here.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 2 , March 1997 , pp. 193 - 217
Copyright
© Cambridge Philosophical Society 1997

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