Groups with exponent six

Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups w ith exponent six are finite. We investigate the nature of relations require d to provide proofs of finiteness for some groups with exponent six. We giv e upper and lower bounds for the number of sixth powers needed to define th e largest 2-generator group with exponent six. We solve related questions a bout other groups with exponent sis using substantial computations which we explain.