Automorphism groups of superextensions of groups
Journal Title: Математичні Студії - Year 2017, Vol 48, Issue 2
Abstract
A family L of subsets of a set X is called {\em linked} if A∩B≠∅ for all A,B∈L. A linked family M is {\em maximal linked} if M coincides with each linked family L on X that contains M. The superextension λ(X) consists of all maximal linked families on X. Any associative binary operation :X×X→X can be extended to an associative binary operation :λ(X)×λ(X)→λ(X). In the paper we study isomorphisms of superextensions of groups and prove that two groups are isomorphic if and only if their superextensions are isomorphic. Also we describe the automorphism groups of superextensions of all groups of order ≤5.
Authors and Affiliations
Taras Banakh, Volodymyr Gavrylkiv
Keywords
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- EP ID EP302486
- DOI 10.15330/ms.48.2.134-142
- Views 56
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