On the lattice of subgroups normalized by the symmetric group in a complete monomial group

We consider a lattice of subgroups normalized by the symmetric group S_n in a complete monomial group G = H|S_n, where H is an arbitrary (finite or infinite) group. It is shown that for n3, the subgroup is strongly paranormal in this wreath product for any H. A similar result is obtained for the alternating group A_n, n4. The property of strong paranormality for D in G means that for any element x G, the commutator identity x,D],D]=x, D] holds. This guarantees a standard arrangement of subgroups of G normalized by D. Bibliography: 17 titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 111–118.