The lattice of algebraic closure operators on an infinite subgroup lattice

• Published in: Communications in algebra Vol. 49; no. 7; pp. 2906 - 2915
• Main Authors: Kilpack, Martha L. H., Magidin, Arturo
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 18.06.2021; Taylor & Francis Ltd
• Subjects: Algebra; Closure operator; Group theory; Operators; Primary 06A15; Secondary 20D30; subgroup lattice; Subgroups

We say a lattice L is a subgroup lattice if there exists a group G such that where is the lattice of subgroups of G, ordered by inclusion. We prove that the lattice of algebraic closure operators which act on the subgroup lattice of an infinite group is itself a subgroup lattice if and only if the g...