NONSOLVABLE GROUPS ALL OF WHOSE CHARACTER DEGREES ARE ODD-SQUARE-FREE

作者：Lewis Mark L; White Donald L^*

来源：Communications in Algebra, 2011, 39(4): 1273-1292.

DOI：10.1080/00927871003652652

• Character degrees
• Nonsolvable groups
• Simple groups
• Square-free

A finite group G is odd-square-free if no irreducible complex character of G has degree divisible by the square of an odd prime. We determine all odd-square-free groups G satisfying S <= G <= Aut(S) for a finite simple group S. More generally, we show that if G is any nonsolvable odd-square-free group, then G has at most two nonabelian chief factors and these must be simple odd-square-free groups. If the alternating group A(7) is involved in G, the structure of G can be further restricted.

• 出版日期2011