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[in Journal: Journal of Algebra and Its Applications] AND [Keyword: Rings] (8)	2 Apr 2025	Run
[in Journal: Chinese Annals of Mathematics] AND [Keyword: Orbit] (1)	2 Apr 2025	Run
[in Journal: Journal of Mathematical Logic] AND [Keyword: Rings] (1)	2 Apr 2025	Run
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articleNo Access
THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS
- YONGCAI REN and
- XIANGYANG LI
Chinese Annals of Mathematics01 Oct 2000
Preview Abstract
Let G be a nonabelian finite group. Then Irr(G/G') is an abelian group under the multiplication of characters and acts on the set of non-linear irreducible characters of G via the multiplication of characters. The purpose of this paper is to establish some facts about the action of linear character group on non-linear irreducible characters and determine the structures of groups G for which either all the orbit kernels are trivial orthe number of orbits is at most two. Using the established results on this action, it is very easy to classify groups G having at most three non-linear irreducible characters.

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