Vol. 23, No. 2, 1967

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Two solvability theorems

I. Martin (Irving) Isaacs

Vol. 23 (1967), No. 2, 281–290

In this paper we prove two theorems which have certain similarities.

Theorem I. Let G be a group with a cyclic Sp subgroup P such that every p’-subgroup of G is abelian. Then either G has a normal p-complement or else PΔG.

Theorem II. Let G be a group and let p2 and q be primes dividing |G|. Suppose for every H < G which is not a q-group or a q’-group that p||H|. If qa is the q-part of |G| and p > qa 1 or if p = qa 1 and an Sp of G is abelian then no primes but p and q divide |G|.

Mathematical Subject Classification
Primary: 20.25
Received: 8 August 1966
Published: 1 November 1967
I. Martin (Irving) Isaacs