Glasgow Mathematical Journal

Research Article

Metacyclic p-groups and their conjugacy classes of subgroups

Rolf Brandla1 and Libero Verardia2 p1

a1 Mathematisches Institut Am Hubland 12 D-W-8700 Würzburg Germany

a2 Dipartimento Di Matematica Piazza di Porta San Donato, 5 I-40127 Bologna Italy

Let G be a group and let ℓ(G) be the set of all conjugacy classes [H] of subgroups H of G, where a partial order ≤ is defined by [H1] ≤ [H2] if and only if H1, is contained in some conjugate of H2.

A number of papers (see for example [1] and the references mentioned there) deal with the question of characterizing groups G by the poset ℓ(G). For example, in [1] it was shown that if ℓ(G) and ℓ(H) are order-isomorphic and G is a noncyclic p-group then |G| = |H|. Moreover, if G is abelian, then G = H, and if G is metacyclic then H is metacyclic.

(Received April 23 1992)


p1 Work supported by M.U.R.S.T. of Itay.