SUBGROUPS OF 3-TRANSPOSITION GROUPS GENERATED BY FOUR 3-TRANSPOSITIONS

Abstract

In this paper we study the subgroups of 3-transposition groups generated by a set of four 3-transpositions. As a consequence we deduce that the smallest Fischer simple group F ₂₂ cannot be generated by four 3-transpositions and hence rank (F ₂₂: D) = 5 or 6, where D is the conjugacy class of 3-transpositions in F ₂₂ and rank (F ₂₂: D) denotes the minimum number of 3-transpositions in D generating F ₂₂. This result is an extension of the work done by the author in [11].