Prime Factors of π-Partial Character Degrees and Conjugacy Class Sizes of π-Elements
Copyright policy )Prime Factors of π-Partial Character Degrees and Conjugacy Class Sizes of π-Elements
Let G be a finite solvable group. We prove that any prime dividing any irreducible π-partial character degree of G divides the size of some conjugacy class of π-elements of G. Under certain hypothesis, we show that if two distinct primes r and s both divide some irreducible π-partial character degree, then there exists a conjugacy class of π-elements whose size is divisible by rs.
Ordinary representations and characters, character degrees, Modular representations and characters, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, \(\pi\)-elements, Arithmetic and combinatorial problems involving abstract finite groups, finite groups, irreducible partial characters, Conjugacy classes for groups, conjugacy classes
Ordinary representations and characters, character degrees, Modular representations and characters, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, \(\pi\)-elements, Arithmetic and combinatorial problems involving abstract finite groups, finite groups, irreducible partial characters, Conjugacy classes for groups, conjugacy classes
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