Some Maximal Subgroups of Infinite Symmetric Groups
نویسنده
چکیده
THIS paper concerns maximal subgroups of symmetric groups on infinite, usually countable, sets. Our main aim is to give examples of maximal subgroups which could claim to be almost stabilisers of familiar combinatorial structures. We emphasise that maximal subgroup always means maximal proper subgroup. Throughout this paper, Cl will denote an infinite set, usually countable. The power set of Q is denoted by 0*(Q). A moiety of a set Q of infinite cardinality K is a subset TofD. such that |F| = |Q\r | = K. The full (unrestricted) symmetric group on Q. is denoted by 5 = Sym (Q). We write (G, Q) for a permutation group G on a set fl. Permutations act on the right, and if a e Q and g e G then a denotes the image of a under g. The support of g is supp(g):={a e Cl: a ¥> a).
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