NDLI: Recognition of $$\text {PSL}(2,p)$$ by order and some information on its character degrees where $$p$$ is a prime

Content Provider	Springer Nature Link
Author	Khosravi, Behnam Khosravi, Behrooz Khosravi, Bahman
Copyright Year	2013
Abstract	Let $$G$$ be a finite group and $$\text {cd}(G)$$ be the set of irreducible character degrees of $$G$$ . In this paper we prove that if $$p$$ is a prime number, then the simple group $$\text {PSL}(2,p)$$ is uniquely determined by its order and some information about its character degrees. In fact we prove that if $$G$$ is a finite group such that (i) $$\|G\|=\|\text {PSL}(2,p)\|$$ , (ii) $$p\in \text {cd}(G)$$ , (iii) $$\text {cd}(G)$$ has an even integer, and (iv) there does not exist any element $$a\in \text {cd}(G)$$ such that $$2p\mid a$$ , then $$G\cong \text {PSL}(2,p)$$ . As a consequence of our result we get that $$\text {PSL}(2,p)$$ is uniquely determined by its order and the largest and the second largest character degrees.
Ending Page	282
Page Count	6
Starting Page	277
File Format	PDF
ISSN	00269255
e-ISSN	14365081
Journal	Monatshefte für Mathematik
Issue Number	2
Volume Number	175
Language	English
Publisher	Springer Vienna
Publisher Date	2013-10-23
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Order Ordinary representations and characters Finite simple groups and their classification Character degrees Mathematics Projective special linear group Recognition Arithmetic and combinatorial problems
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Recognition of $$\text {PSL}(2,p)$$ by order and some information on its character degrees where $$p$$ is a prime