A new characterization for some extensions of PSL(2,p) by order and some character degrees

作者：Khosravi Behrooz; Khosravi Behnam; Khosravi Bahman

来源：Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 2017, 60(3): 267-275.

• Character degrees
• order
• projective special linear group
• characterization

Many authors were recently concerned with the following question: What can be said about the structure of a finite group G, if some information is known about the arithmetical structure of the degrees of the irreducible characters of G?
Let G be a finite group and X-1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Let p be an odd prime number and M = PGL(2,p), M = Z(2) X PSL(2,p) or M = SL(2,p).
In this paper we prove that M is uniquely determined by its order and some information on its character degrees. As a consequence of our results we prove that if G is a finite group such that X1 (G) = X1(M), then G congruent to M. This implies that M is uniquely determined by the structure of its complex group algebra.

• 出版日期2017