Nonsolvable Groups Satisfying the One-prime Hypothesis
Source: Algebras and Representation Theory, Volume 10, Number 4, August 2007 , pp. 379-412(34)
Abstract:Recall that a finite group G satisfies the one-prime hypothesis if the greatest common divisor for any pair of distinct degrees in cd(G) is either 1 or a prime. In this paper, we classify the nonsolvable groups that satisfy the one-prime hypothesis. As a consequence of our classification, we show that if G is a nonsolvable group satisfying the one-prime hypothesis, then |cd(G)| ≤ 8, and hence, if G is any group satisfying the one-prime hypothesis, then |cd(G)| ≤ 9.
Document Type: Research article
Publication date: 2007-08-01