Powers of characters of finite groups

Zvi Arad, David Chillag, Marcel Herzog

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


LetG be a finite group and θ a complex character ofG. Define Irr(θ) to be the set of all irreducible constituents of θ andIrr(G) to be the set of all irreducible characters ofG. Thecharacter-covering number of a finite groupG, ccn(G), is defined as the smallest positive integer m such thatIrr(χm) =Irr(G) for allχ∈Irr(G)-{1G}. If no such positive integer exists we say that the character-covering-number ofG is infinite. In this article we show that a finite nontrivial groupG has a finite character-covering-number if and only ifG is simple and non-abelian and ifG is a nonabelian simple group thenccn(G) ≤ k2 - 3k + 4, wherek is the number of conjugacy classes ofG. Then we show (using the classification of the finite simple groups) that the only finite group with a character-covering-number equal to two is the smallest Janko's group,J1. These results are analogous to results obtained previously concerning the covering of groups by powers of conjugacy classes. Other related results are shown.

Original languageEnglish
Pages (from-to)241-255
Number of pages15
JournalJournal of Algebra
Issue number1
StatePublished - 1 Oct 1986


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