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Finite groups with many p-regular conjugacy classes.
- Source :
-
Journal of Algebra . Mar2024, Vol. 641, p716-734. 19p. - Publication Year :
- 2024
-
Abstract
- Let G be a finite group and let p be a prime. In this paper, we study the structure of finite groups with a large number of p -regular conjugacy classes or, equivalently, a large number of irreducible p -modular representations. We prove sharp lower bounds for this number in terms of p and the p ′ -part of the order of G which ensure that G is p -solvable. A bound for the p -length is obtained which is sharp for odd primes p. We also prove a new best possible criterion for the existence of a normal Sylow p -subgroup in terms of these quantities. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 641
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 174508301
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2023.11.010