Affiliation:
1. FB Mathematik , TU Kaiserslautern , Postfach 3049, 67653 Kaiserslautern , Germany
2. Department of Physics, Informatics and Mathematics , National Academy of Sciences of Belarus , Minsk , Belarus
Abstract
Abstract
Let G be a finite group and, for a prime p, let S be a Sylow p-subgroup of G.
A character χ of G is called
Syl
p
{\mathrm{Syl}_{p}}
-regular if the restriction of χ to S is the character of the regular representation of S.
If, in addition, χ vanishes at all elements of order divisible by p, χ is said to be Steinberg-like.
For every finite simple group G, we determine all primes p for which G admits a Steinberg-like character, except for alternating groups in characteristic 2.
Moreover, we determine all primes for which G has a projective FG-module of dimension
|
S
|
{\lvert S\rvert}
, where F is an algebraically closed field of characteristic p.
Subject
Algebra and Number Theory
Reference24 articles.
1. J. Conway, R. Curtis, S. Norton, R. Parker and R. Wilson,
Atlas of Finite Groups,
Clarendon Press, Oxford, 1985.
2. C. W. Curtis and I. Reiner,
Methods of Representation Theory with Applications to Finite Groups and Orders,
Wiley, New York, 1990.
3. L. Emmett and A. E. Zalesski,
On regular orbits of elements of classical groups in their permutation representations,
Comm. Algebra 39 (2011), 3356–3409.
4. W. Feit,
The Representation Theory of Finite Groups,
North-Holland, Amsterdam, 1982.
5. E. Giannelli and S. Law,
On permutation characters and Sylow p-subgroups of 𝔖n{\mathfrak{S}_{n}},
J. Algebra 506 (2018), 409–428.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献