The lattice of closure operators on a subgroup lattice

We say a lattice L is a subgroup lattice if there exists a group G such that Sub(G)[approx equal to]L, where Sub(G) is the lattice of subgroups of G, ordered by inclusion. We prove that the lattice of closure operators which act on the subgroup lattice of a finite group G is itself a subgroup lattic...

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Bibliographic Details
Published inCommunications in algebra Vol. 46; no. 4; pp. 1387 - 1396
Main Authors Kilpack, Martha L. H., Magidin, Arturo
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis Ltd 03.04.2018
Subjects
Operators
Subgroups
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Summary:We say a lattice L is a subgroup lattice if there exists a group G such that Sub(G)[approx equal to]L, where Sub(G) is the lattice of subgroups of G, ordered by inclusion. We prove that the lattice of closure operators which act on the subgroup lattice of a finite group G is itself a subgroup lattice if and only if G is cyclic of prime power order.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2016.1255893