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Group Characters and Normal Hall Subgroups

Published online by Cambridge University Press:  22 January 2016

P. X. Gallagher
P. X. Gallagher*
Affiliation:
Massachusetts Institute of Technology and Paris, France
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Let G be a finite group and let ψ be an (ordinary) irreducible character of a normal subgroup N. If ψ extends to a character of G then ψ is invariant under G, but the converse is false. In section 3 it is shown that if ψ extends coherently to the intermediate groups H for which H/N is elementary, then ψ extends to G. If N is a Hall subgroup, then in order for ψ to extend to G it is sufficient that ψ be invariant under G. This leads to a construction of the characters of G from the characters of N and the characters of the subgroups of G/N in this case.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 21 , December 1962 , pp. 223 - 230
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1962

References

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