Closed hulls in infinite symmetric groups
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 by Franklin Haimo PDF
 Trans. Amer. Math. Soc. 180 (1973), 475484 Request permission
Abstract:
Let $\operatorname {Sym} M$ be the symmetric group of an infinite set $M$. What is the smallest subgroup of $\operatorname {Sym} M$ containing a given element if the subgroup is subject to the further condition that it is also the automorphism group of some finitary algebra on $M$? The structures of such closed hulls are related to the disjointcycle decompositions of the given elements. If the closed hull is not just the cyclic subgroup on the given element then it is nonminimal as a closed hull and is represented as a subdirect product of finite cyclic groups as well as by a quotient group of a group of infinite sequences. We determine the conditions under which it has a nontrivial primary component for a given prime $p$ and show that such components must be bounded abelian groups.References

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Additional Information
 © Copyright 1973 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 180 (1973), 475484
 MSC: Primary 20E99
 DOI: https://doi.org/10.1090/S00029947197303220656
 MathSciNet review: 0322065