Affiliation:
1. Dipartimento di Matematica e Informatica , Università degli Studi di Firenze , Firenze , Italy
Abstract
Abstract
If a group G is π-separable, where π is a set of primes, the set of irreducible characters
B
π
(
G
)
∪
B
π
′
(
G
)
{\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(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
B
π
(
G
)
∪
B
π
′
(
G
)
{\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)}
.
Subject
Algebra and Number Theory
Reference12 articles.
1. S. Dolfi, E. Pacifici, L. Sanus and P. Spiga,
On the orders of zeros of irreducible characters,
J. Algebra 321 (2009), 345–352.
2. D. Gajendragadkar,
A characteristic class of characters finite of π-separable groups,
J. Algebra 59 (1979), 237–259.
3. K. W. Gruenberg and K. W. Roggenkamp,
Decomposition of the augmentation ideal and of the relation modules of a finite group,
Proc. Lond. Math. Soc. 31 (1975), 149–166.
4. I. M. Isaacs,
Character Theory of Finite Groups,
Academic Press, New York, 1976.
5. I. M. Isaacs,
Characters of π-separable groups,
J. Algebra 86 (1984), 98–128.