Vol. 24, No. 3, 1968

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A characterization of groups in terms of the degrees of their characters. II

I. Martin (Irving) Isaacs and Donald Steven Passman

Vol. 24 (1968), No. 3, 467–510

In this paper we continue our study of the relationship between the structure of a finite group G and the set of degrees of its irreducible complex characters. The following hypotheses on the degrees are considered: (A) G has r.x. e for some prime p, i.e. all the degrees divide pe, (B) the degrees are linearly ordered by divisibility and all except 1 are divisible by exactly the same set of primes, (C) G has a.c. m, i.e., all the degrees except 1 are equal to some fixed m, (D) all the degrees except 1 are prime (not necessarily the same prime) and (E) all the degrees except 1 are divisible by pe > p but none is divisible by pe+1. In each of these situations, group theoretic information is deduced from the character theoretic hypothesis and in several cases complete characterizations are obtained.

Mathematical Subject Classification
Primary: 20.25
Received: 28 December 1966
Published: 1 March 1968
I. Martin (Irving) Isaacs
Donald Steven Passman