Nonperiodic groups in which all decomposable pd-subgroups are normal (Q1263671)

Let G be a group and p a prime. In the author's terminology: a pd- subgroup is a subgroup having an element of order p; G is a \(di_ p\)- group when G has a pd-subgroup decomposable as a non-trivial direct product and all such subgroups are normal in G; G is a pdI-group when G has a pd-subgroup and all such subgroups are normal in G. The main theorem of the paper classifies non-periodic non-abelian \(di_ p\)-groups into six types. The description of these types is too complex to reproduce, but generally involves cyclic extensions of pdI- or abelian groups. The proof proceeds by a series of ten technical lemmas.