A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if G is a group and H is a subgroup of finite index of G, the index |G : H| cannot be recognized in the lattice L(G) of all subgroups of G, as for instance all groups of prime order have isomorphic subgroup lattices. The aim of this paper is to give a lattice-theoretic characterization of the number of prime factors (with multiplicity) of |G : H|.

Detecting the index of a subgroup in the subgroup lattice

DE FALCO, MARIA;DE GIOVANNI, FRANCESCO;MUSELLA, CARMELA;
2005

Abstract

A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if G is a group and H is a subgroup of finite index of G, the index |G : H| cannot be recognized in the lattice L(G) of all subgroups of G, as for instance all groups of prime order have isomorphic subgroup lattices. The aim of this paper is to give a lattice-theoretic characterization of the number of prime factors (with multiplicity) of |G : H|.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/311990
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