A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant characters for finite reflection groups, nilpotent groups and complete monomial groups. We also propose some conjectures about the structure of the groups admitting such characters.
Pellegrini, M. A., Irreducible p-constant characters of finite reflection groups, <<JOURNAL OF GROUP THEORY>>, 2017; 20 (5): 911-923. [doi:10.1515/jgth-2016-0059] [http://hdl.handle.net/10807/105327]
Irreducible p-constant characters of finite reflection groups
Pellegrini, Marco AntonioPrimo
2017
Abstract
A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant characters for finite reflection groups, nilpotent groups and complete monomial groups. We also propose some conjectures about the structure of the groups admitting such characters.
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