Vol. 83, No. 1, 1979

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Finite groups with small unbalancing 2-components

Robert Hugh Gilman and Ronald Mark Solomon

Vol. 83 (1979), No. 1, 55–106

In this paper we supply one link in a chain of results which will prove the following two conjectures:

B(G)-Conjecture. If H is a 2-local subgroup of a finite group G, then [L(H),O(H)] O(G).

Unbalanced Group Conjecture. If G is a finite group with O(CG(t))⊈O(G) for some involution t G, then O(CG(t)) acts nontrivially on L∕Z(L) where L is a 2-component of G with L∕Z(L) isomorphic to one of the following simple groups:

  1. A simple Chevalley group or twisted variation over a field of odd order;
  2. An alternating group of odd degree;
  3. PSL (3,4) of He, the simple group of Held.

Mathematical Subject Classification 2000
Primary: 20D05
Received: 25 July 1977
Revised: 2 October 1978
Published: 1 July 1979
Robert Hugh Gilman
Ronald Mark Solomon
Department of Mathematics
The Ohio State University
231 West 18th Avenue
Columbus OH 43210–1174
United States