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The largest character degree, conjugacy class size and subgroups of finite groups

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ABSTRACT Let G be a finite group, let b(G) denote the largest irreducible character degree of the group G and let bcl(G) denote the largest conjugacy class size of the… Click to show full abstract

ABSTRACT Let G be a finite group, let b(G) denote the largest irreducible character degree of the group G and let bcl(G) denote the largest conjugacy class size of the group G. We study the relations between the sizes of the nilpotent and solvable subgroups of G and b(G). We also study the relations between the sizes of the nilpotent and solvable subgroups of G and bcl(G).

Keywords: conjugacy class; character degree; class size

Journal Title: Communications in Algebra
Year Published: 2018

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