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
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