Finite groups with a special 2-generator property

Tuval S. Foguel

Vol. 170 (1995), No. 2, 483–495

DOI: 10.2140/pjm.1995.170.483

Abstract

This paper deals with finite groups. J. L. Brenner and James Wiegold defined a finite group G as lying in Γ₁⁽²⁾ if G is nonabelian and for every 1≠x ∈ G, either x is an involution and G = ⟨x,y⟩ for some y ∈ G or x is not an involution and there is an involution z ∈ G with G = ⟨x,z⟩. In this paper we expand the work of J. L. Brenner and James Wiegold, and that of Martin J. Evans in the investigation of which finite groups lie in Γ₁⁽²⁾.

Mathematical Subject Classification 2000

Primary: 20D10

Secondary: 20D06, 20F05

Milestones

Received: 22 March 1993

Revised: 30 November 1993

Published: 1 October 1995