Fusions of character tables and Schur rings of abelian groups

Stephen P. Humphries, Kenneth Johnson

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

If the character table of a finite group H satisfies certain conditions, then the classes and characters of H can fuse to give the character table of a group G of the same order. We investigate the case where H is an abelian group. The theory is developed in terms of the S-rings of Schur and Wielandt. We discuss certain classes of p-groups which fuse from abelian groups and give examples of such groups which do not. We also show that a large class of simple groups do not fuse from abelian groups. The methods to show fusion include the use of extensions which are Camina pairs, but other techniques on S-rings are also developed.

Original languageEnglish (US)
Pages (from-to)1437-1460
Number of pages24
JournalCommunications in Algebra
Volume36
Issue number4
DOIs
StatePublished - Apr 1 2008

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Schur Ring
Character Table
Abelian group
Fusion
Ring
Simple group
P-groups
Finite Group
Class

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Humphries, Stephen P. ; Johnson, Kenneth. / Fusions of character tables and Schur rings of abelian groups. In: Communications in Algebra. 2008 ; Vol. 36, No. 4. pp. 1437-1460.
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Fusions of character tables and Schur rings of abelian groups. / Humphries, Stephen P.; Johnson, Kenneth.

In: Communications in Algebra, Vol. 36, No. 4, 01.04.2008, p. 1437-1460.

Research output: Contribution to journalArticle

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