The representation type of the character ring

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International Electronic Journal of Algebra
Volume:23 Issue:23
The representation type of the character ring

The representation type of the character ring

Pages : 47-114

View : 34 | Download : 8

Publication Date : 2018-01-11

Article Type : Research Paper

Abstract :Let Rinsert ignore into journalissuearticles values(G); be the character ring of a nite group G. We consider the question whether the representation type of Rinsert ignore into journalissuearticles values(G); is nite or in nite. We show that if Rinsert ignore into journalissuearticles values(G); is representation- nite, then expinsert ignore into journalissuearticles values(G); is cube-free and the Sylow subgroups of G are cyclic, elementary-abelian, or nonabelian of order 8. Moreover, we give further necessary as well as some sucient conditions on the structure of G for the niteness of the representation type of Rinsert ignore into journalissuearticles values(G);.
Keywords : Character ring, representation type, almost 2 transitive groups of cube free order

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