Nonsolvable Groups Satisfying the One-prime Hypothesis

Authors: Lewis, Mark¹; White, Donald²

Source: Algebras and Representation Theory, Volume 10, Number 4, August 2007 , pp. 379-412(34)

Publisher: Springer

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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.

Keywords: One-prime hypothesis; Finite group; Irreducible characters; 20c15

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10468-007-9057-2

Affiliations: 1: Email: lewis@math.kent.edu 2: Email: white@math.kent.edu

Publication date: 2007-08-01