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- W2068532673 abstract "Let ( S , ≤) be a poset (partially ordered set), A ( S ) = Aut( S , ≤) its automorphism group and G ⊆ A ( S ) a subgroup. In the literature, various authors have studied sufficient conditions on G and the structure of ( S , ≤) which imply that G is simple or perfect. Let us call ( S , ≤) doubly homogeneous if each isomorphism between two 2-subsets of 5 extends to an isomorphism of ( S , ≤). Higman [8] proved that if ( S , ≤) is a doubly homogeneous chain then B ( S ), the group of all automorphisms of ( S , ≤) with bounded support, is simple, and each element of B ( S ) is a commutator in B ( S ). Droste, Holland and Macpherson [5] showed that if ( S , ≤) is a doubly homogeneous tree then its automorphism group again contains a unique simple normal subgroup in which each element is a commutator. Dlab [3] established similar results for various groups of locally linear automorphisms of the reals. Further results in this direction are contained in Glass [7]. It is the aim of this note to establish a common generalization and sharpening of the previously mentioned results." @default.
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- W2068532673 date "1991-01-01" @default.
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- W2068532673 title "Commutators in groups of order-preserving permutations" @default.
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