Groups whose elements have given orders

Abstract

'ELEMENT orders' is one of the most fundamental concepts in group theory. It plays an impor-tant role in the research of group theory, which can be seen from the famous Burnside’s prob-lem. Some well-known group theory specialists, such as Neumann, Higman, Suzuki and oth-ers, have studied the groups whose element orders take the special values. In 1981 wediscussed the finite groups of all those whose elements are of prime order except identity ele-