POWER-COMMUTATOR STRUCTURE OF FINITE RHO-GROUPS

For a finite p-group G, Gn is the n-ih element in the descending central series of G; P(G) is the subgroup of G generated by the set of all for x belonging to G; and is the Frattini subgroup of G. we examine some connections between the property and regularity, and obtain a characterization of regular 3-groups (Theorem 4). In we obtain bounds onthe number of generators of various commutator subgroups of G in the. © 1969 by Pacific Journal of Mathematics.