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Lookup NU author(s): Dr John Britnell
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Let G be a finite group and H a normal subgroup such that G/H is cyclic. Given a conjugacy class gG of G, we define its centralizing subgroup to be HCG(g). Let K be such that H ≤ K ≤ G. We show that the G-conjugacy classes contained in K whose centralizing subgroup is K are equally distributed between the cosets of H in K. The proof of this result is entirely elementary. As an application, we find expressions for the number of conjugacy classes of K under its own action, in terms of quantities relating only to the action of G. © 2008 London Mathematical Society.
Author(s): Britnell JR, Wildon M
Publication type: Article
Publication status: Published
Journal: Bulletin of the London Mathematical Society
Year: 2008
Volume: 40
Issue: 5
Pages: 897-906
Print publication date: 01/10/2008
ISSN (print): 0024-6093
ISSN (electronic): 1469-2120
Publisher: Oxford University Press
URL: http://dx.doi.org/10.1112/blms/bdn073
DOI: 10.1112/blms/bdn073
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