Remarks On Finite Groups Defined By Generating Relations

Abstract

1. Introduction. After establishing aduplication principle(§2) which enables us to derive a group of order 2h with k + 1 involutory generators from any group of order h with k generators, we shall prove the followingcombination principle :Letandbe two groups, each havingkgenerators, such that the rth generators ofandhave relatively prime periods for each r from 1 to k.