Vol. 36, No. 3, 1971

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The p-parts of character degrees in p-solvable groups

I. Martin (Irving) Isaacs

Vol. 36 (1971), No. 3, 677–691

Let G be a finite group and Irr(G) the set of irreducible complex characters of G. Fix a prime integer p and let e(G) be the largest integer such that pe(G) divides χ(1) for some χ Irr(G). The purpose of this paper is to obtain information about the structure of G, and in particular about a Sylow p-subgroup of G, from a knowledge of e(G). If G is solvable, we obtain the bound 2e(G) + 1 for the derived length of an Sp subgroup of G. We also obtain some information about the normal structure of G in terms of e(G).

Mathematical Subject Classification 2000
Primary: 20C15
Received: 6 October 1969
Published: 1 March 1971
I. Martin (Irving) Isaacs