NDLI: Recognition of the simple group PSL( $$2,p^{2}$$ ) by character degree graph and order

Content Provider	Springer Nature Link
Author	Khosravi, Behnam Momen, Zahra Khosravi, Behrooz Khosravi, Bahman
Copyright Year	2014
Abstract	Let $$G$$ be a finite group. The character degree graph of $$G$$ , which is denoted by $$\Gamma (G)$$ , is the graph whose vertices are the prime divisors of the character degrees of the group $$G$$ and two vertices $$p_1$$ and $$p_2$$ are joined by an edge if $$p_1p_2$$ divides some character degree of $$G$$ . In this paper we prove that the simple group $$\mathrm{PSL}(2,p^2) $$ is uniquely determined by its character degree graph and its order. Let $$X_1(G)$$ be the set of all irreducible complex character degrees of $$G$$ counting multiplicities. As a consequence of our results we prove that if $$G$$ is a finite group such that $$X_1(G)=X_1(\mathrm{PSL}(2,p^2) )$$ , then $$G\cong \mathrm{PSL}(2,p^2) $$ . This implies that $$\mathrm{PSL}(2,p^2) $$ is uniquely determined by the structure of its complex group algebra.
Ending Page	257
Page Count	7
Starting Page	251
File Format	PDF
ISSN	00269255
e-ISSN	14365081
Journal	Monatshefte für Mathematik
Issue Number	2
Volume Number	178
Language	English
Publisher	Springer Vienna
Publisher Date	2014-08-21
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Order Ordinary representations and characters Character degree graph Finite simple groups and their classification Mathematics Projective special linear group Recognition Arithmetic and combinatorial problems
Content Type	Text
Resource Type	Article
Subject	Mathematics

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