Geodesic
On the lattice of subgroups normalized by a symmetric one in the complete monomial group
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 111-118 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a lattice of subgroups normalized by a symmetric group $S_n$ in the complete monomial group $G=H\wr S_n$ where $H$ is an arbitrary (finite or infinite) group. It is shown that for $n\ge3$ the subgroup is strongly paranormal in this wreath product for any $H$. A similar result is obtained for an alternating group $A_n$, $n\ge4$. The property of strong paranormality for $D$ in $G$ means that for any element $x\in G$ the commutator identity $[[x,D],D]=[x,D]$ holds. That condition garantees a standard arrangement of subgroups of $G$ normalized by $D$. 
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V. I. Mysovskikh. On the lattice of subgroups normalized by a symmetric one in the complete monomial group. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 111-118. http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a12/

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