A new characterization for the simple group PSL ( 2 , p 2 ) by order and some character degrees

Behrooz Khosravi; Behnam Khosravi; Bahman Khosravi; Zahra Momen

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 1, page 271-280
  • ISSN: 0011-4642

Abstract

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Let G be a finite group and p a prime number. We prove that if G is a finite group of order | PSL ( 2 , p 2 ) | such that G has an irreducible character of degree p 2 and we know that G has no irreducible character θ such that 2 p ∣ θ ( 1 ) , then G is isomorphic to PSL ( 2 , p 2 ) . As a consequence of our result we prove that PSL ( 2 , p 2 ) is uniquely determined by the structure of its complex group algebra.

How to cite

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Khosravi, Behrooz, et al. "A new characterization for the simple group ${\rm PSL}(2,p^2)$ by order and some character degrees." Czechoslovak Mathematical Journal 65.1 (2015): 271-280. <http://eudml.org/doc/270042>.

@article{Khosravi2015,
abstract = {Let $G$ be a finite group and $p$ a prime number. We prove that if $G$ is a finite group of order $|\{\rm PSL\}(2,p^2)|$ such that $G$ has an irreducible character of degree $p^2$ and we know that $G$ has no irreducible character $\theta $ such that $2p\mid \theta (1)$, then $G$ is isomorphic to $\{\rm PSL\}(2,p^2)$. As a consequence of our result we prove that $\{\rm PSL\}(2,p^2)$ is uniquely determined by the structure of its complex group algebra.},
author = {Khosravi, Behrooz, Khosravi, Behnam, Khosravi, Bahman, Momen, Zahra},
journal = {Czechoslovak Mathematical Journal},
keywords = {character degree; order; projective special linear group},
language = {eng},
number = {1},
pages = {271-280},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new characterization for the simple group $\{\rm PSL\}(2,p^2)$ by order and some character degrees},
url = {http://eudml.org/doc/270042},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Khosravi, Behrooz
AU - Khosravi, Behnam
AU - Khosravi, Bahman
AU - Momen, Zahra
TI - A new characterization for the simple group ${\rm PSL}(2,p^2)$ by order and some character degrees
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 271
EP - 280
AB - Let $G$ be a finite group and $p$ a prime number. We prove that if $G$ is a finite group of order $|{\rm PSL}(2,p^2)|$ such that $G$ has an irreducible character of degree $p^2$ and we know that $G$ has no irreducible character $\theta $ such that $2p\mid \theta (1)$, then $G$ is isomorphic to ${\rm PSL}(2,p^2)$. As a consequence of our result we prove that ${\rm PSL}(2,p^2)$ is uniquely determined by the structure of its complex group algebra.
LA - eng
KW - character degree; order; projective special linear group
UR - http://eudml.org/doc/270042
ER -

References

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