Simple groups and a Diophantine equation
Leo J. Alex · Pacific Journal of Mathematics · 1983
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 /^-subgroup in its normalizer is three in G. Suppose the degree equation for the principal />-b!ock, B 0 (p), has the form 1+ 2 a = 3*5 C + 2*3 e 5 / where a, b, c, d, e and / 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), C/(3,3), L(3,4) and A s .This is accomplished by solving the exponential Diophantine degree equation for B Q (p).