The lattice of closure operators on a subgroup lattice |
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| Authors: | Martha L H Kilpack |
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| Institution: | 1. Department of Mathematics, Computer Science and Statistics, State University of New York College at Oneonta, Oneonta, New York, USA;2. Department of Mathematics, Brigham Young University, Provo, Utah, USA |
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| Abstract: | We say a lattice L is a subgroup lattice if there exists a group G such that Sub(G)?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. |
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| Keywords: | Closure operators lattice subgroups |
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