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Manfred Droste, W. Charles Holland

Generating automorphism groups of chains

Let (?, ?) be any doubly homogeneous chain and Aut(?) its group of order-automorphisms. We show that if J is a set of generators of Aut(?), then there is a positive integer n such that every element of Aut(?) is a product of at most n members of J ? J^?1. Also, Aut(?) cannot be written as the union of a countable chain of proper subgroups of Aut(?).

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 17, 05/2005
Pages: 699 - 710

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