An algorithm for the Thompson subgroup of a p-group

For a p-group P, p a prime, there are two versions of the Thompson subgroup of P  , namely the elementary version Je(P)Je(P) and the non-elementary version J(P)J(P). This paper describes algorithms for calculating these two subgroups. Depending on P  , these algorithms are effective for groups of order up to p30p30. By modifying these algorithms we also produce algorithms for K(P)K(P), a further characteristic subgroup also introduced by Thompson [20], and characteristic subgroups D(P)D(P) and De(P)De(P) introduced by Glauberman and Solomon [12]. Sample calculations using these algorithms are discussed with an accompanying file giving details of these calculations, along with the code for the algorithm.