Counting maximal topologies on countable groups and rings |
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Authors: | D Dikranjan Igor Protasov |
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Institution: | a Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy b Department of Cybernetics, Kiev University, Volodimirska 64, 01033 Kiev, Ukraine |
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Abstract: | Two non-discrete Hausdorff group topologies τ1, τ2 on a group G are called transversal if the least upper bound τ1∨τ2 of τ1 and τ2 is the discrete topology. We show that a countable group G admitting non-discrete Hausdorff group topologies admits c2 pairwise transversal complete group topologies on G (so c2 maximal group topologies). Moreover, every abelian group G admits 2|G|2 pairwise transversal complete group topologies. |
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Keywords: | primary 22A05 54A25 secondary 54H11 |
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