Primitive characters of odd order groups
Copyright policy )Primitive characters of odd order groups
Let $G$ be a finite group of odd order. We show that if $χ$ is an irreducible primitive character of $G$ then for all primes $p$ dividing the order of $G$ there is a conjugacy class such that the $p-$part of $χ(1)$ divides the size of that conjugacy class. We also show that for some classes of groups the entire degree of an irreducible primitive character $χ$ divides the size of a conjugacy class.
10 pages
- University of Manchester United Kingdom
- University of Manchester United Kingdom
Ordinary representations and characters, Representation theory of groups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, FOS: Mathematics, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Group Theory (math.GR), primitive characters, Representation Theory (math.RT), Mathematics - Group Theory, Mathematics - Representation Theory, conjugacy classes
Ordinary representations and characters, Representation theory of groups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, FOS: Mathematics, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Group Theory (math.GR), primitive characters, Representation Theory (math.RT), Mathematics - Group Theory, Mathematics - Representation Theory, conjugacy classes
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