If a group G is π-separable, where π is a set of primes, the set of irreducible characters Bπ(G) ∪ Bπ′(G) can be defined. In this paper, we prove variants of some classical theorems in character theory, namely the theorem of Ito-Michler and Thompson's theorem on character degrees, involving irreducible characters in the set Bπ(G) ∪ Bπ′(G).
Grittini, N., Character degrees in π-separable groups, <<JOURNAL OF GROUP THEORY>>, 2020; 23 (6): 1069-1080. [doi:10.1515/jgth-2019-0186] [http://hdl.handle.net/10807/188778]
Character degrees in π-separable groups
Grittini, Nicola
2020
Abstract
If a group G is π-separable, where π is a set of primes, the set of irreducible characters Bπ(G) ∪ Bπ′(G) can be defined. In this paper, we prove variants of some classical theorems in character theory, namely the theorem of Ito-Michler and Thompson's theorem on character degrees, involving irreducible characters in the set Bπ(G) ∪ Bπ′(G).
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