Generalised Cogrowth series, random walks, and the group determinant
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Published:2017-08-14
Issue:3
Volume:165
Page:445-465
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ISSN:0305-0041
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Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
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language:en
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Short-container-title:Math. Proc. Camb. Phil. Soc.
Author:
HUMPHRIES STEPHEN P.
Abstract
We associate to a groupGa series that generalises the cogrowth series ofGand is related to a random walk onG. We show that the series is rational if and only ifGis finite, generalizing a result of Kouksov [Kou]. We show that whenGis finite, the series determinesG. There are naturally occurring ideals and varieties that are acted on by Aut(G). We study these and generalize this to the context ofS-rings over finite groups. There is an associated representation of Aut(G) and we characterize when this is irreducible.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics
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