Determining group structure from the sets of character degrees

作者：Aziziheris Kamal^*

来源：Journal of Algebra, 2010, 323(6): 1765-1782.

DOI：10.1016/j.jalgebra.2010.01.002

• Solvable groups
• Character degrees
• Fitting subgroup
• Direct product

Let cd(G) be the set of all irreducible complex characters of a finite group G. In [4], Lewis proved that if p. q, r, and s are distinct primes and cd(G) = {1. p, q, r, pq, pr} or cd(G) = {1, p, q. r, s, pr. ps, qr, qs}, then G is the direct product of two normal non-abelian subgroups of G. We generalize Lewis' results by loosening the primeness hypothesis of cd(G).

• 出版日期2010-3-15