A method of Bender applied to groups of J 3-type

Abstract

We apply a method of Bender [H. Bender. Finite groups with large subgroups. Illinois J. Math . 18 (1974), 223–228.] to determine the order of a group G of J 3 -type. Moreover, we determine the local p -structure of G for every prime p dividing the order of G . The results of this paper are obtained by exploiting the action of G on its geometry [B. Baumeister. A geometry for groups of J 3 -type. Arch. Math. ( Basel ) 88 (2007), 491–499.] and by sophisticated use of elementary group theory.