A new characterization for some extensions of PSL(2, q) for some q by some character degrees

作者：Khosravi Behrooz; Khosravi Behnam; Khosravi Bahman

来源：Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2016, 126(1): 49-59.

DOI：10.1007/s12044-015-0257-0

• Characterization
• character degrees
• order
• complex group algebra

In [22] (Tong-Viet H P, Simple classical groups of Lie type are determined by their character degrees, J. Algebra, 357 (2012) 61-68), the following question arose: Which groups can be uniquely determined by the structure of their complex group algebras? The authors in [12] (Khosravi B et al., Some extensions of PSL(2, p(2)) are uniquely determined by their complex group algebras, Comm. Algebra, 43(8) (2015) 3330-3341) proved that each extension of PSL(2, p(2)) of order 2 vertical bar PSL(2, p(2))vertical bar is uniquely determined by its complex group algebra. In this paper we continue this work. Let p be an odd prime number and q = p or q = p(3). Let M be a finite group such that vertical bar M vertical bar = h vertical bar PSL(2, q), where h is a divisor of vertical bar Out(PSL(2, q))vertical bar. Also suppose that M has an irreducible character of degree q and 2p does not divide the degree of any irreducible character of M. As the main result of this paper we prove that M has a unique nonabelian composition factor which is isomorphic to PSL(2, q). As a consequence of our result we prove that M is uniquely determined by its order and some information on its character degrees which implies that M is uniquely determined by the structure of its complex group algebra.

• 出版日期2016-2