On the Group of Weak Automorphisms of a Family of Equivalence Relations

Th. Gschwend and O. H. Kegel ()
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Th. Gschwend: Albert-Ludwigs-Universität, Mathematisches Institut
O. H. Kegel: Albert-Ludwigs-Universität, Mathematisches Institut

A chapter in Algebra and Operator Theory, 1998, pp 237-248 from Springer

Abstract: Abstract Let E be a set of equivalence relations on the set Ω. We call a permutation π of Ω an e-permutation, e ∈ E, if it leaves every a-class of Ω invariant. We consider the set S(E):= ∪ e∈ E S (e) of all E-permutations of Ω or weak automorphisms of E. If E is directed by the natural partial order the set S(E) is a group - the E-symmetric group - our group of weak automorphisms of E. If the family E is well-behaved (homogeneous) and Ω is countable then the class of all E-symmetric groups can be characterised up to permutation-isomorphism by the Steinitz type. Some normal subgroups of S(E) are pointed out.

Keywords: Equivalence Relation; Normal Subgroup; Symmetric Group; Left Coset; Natural Partial Order (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-94-011-5072-9_22

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