2020/04/09 by Williams, James
#20D15 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2004.04610
In this paper, we give elementary proofs of the Restricted Burnside Problem and the Hughes Conjecture for finite p-groups with Hall's regular power structure property. Moreover, in this setting we determine an explicit bound on the order of a finite d-generator p-group of fixed exponent. Further applications of p-groups with regular power structure are presented. For example, we give a short new proof of an important property of powerful p-groups; namely, that the minimal number of generators of a subgroup of such a group G is at most the number needed to generate G.