Vol. 104, No. 2, 1983

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Simple groups and a Diophantine equation

Leo James Alex

Vol. 104 (1983), No. 2, 257–262
Abstract

Let G be a finite simple group whose order is of the form pm where p is a prime, (p,m) = 1, and the index of a Sylow p-subgroup in its normalizer is three in G. Suppose the degree equation for the principal p-block, B0(p), has the form 1 + 2a = 3b5c + 2d3e5f where a, b, c, d, e and f are non-negative integers. In this paper it is shown that under these conditions G must be isomorphic to one of the groups L(2,7), U(3,3), L(3,4) and A8. This is accomplished by solving the exponential Diophantine degree equation for B0(p).

Mathematical Subject Classification 2000
Primary: 20D05
Secondary: 10B25
Milestones
Received: 9 September 1980
Published: 1 February 1983
Authors
Leo James Alex