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The nuclear length of a character

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Wayne W. Wheeler
Wayne W. Wheeler
Affiliation:
School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, (e-mail: wheeler@pell.anu.edu.au)
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Abstract

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If G is a π-separable group and χ is an irreducible character of G, then Issacs gas defined an associated pair (W, γ), called a nucleus of χ. The nucleus is the last term in a certain chain of pairs (I, Ω), where I is a subgroup of G and Ω is an irreducible character of I. The length of this chain is an invariant of χ that we call the nuclear length. In this paper we study bounds on the nuclear length of χ as a function of the π-length of G and as a function of the character degree χ(1).

MSC classification

Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 1 , August 1994 , pp. 49 - 59
Copyright
Copyright © Australian Mathematical Society 1994

References

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