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Cubes of conjugacy classes covering the infinite symmetric group


Author: Manfred Droste
Journal: Trans. Amer. Math. Soc. 288 (1985), 381-393
MSC: Primary 20B07; Secondary 20B30
DOI: https://doi.org/10.1090/S0002-9947-1985-0773066-3
MathSciNet review: 773066
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Abstract: Using combinatorial methods, we prove the following theorem on the group $ S$ of all permutations of a countably-infinte set: Whenever $ p \in S$ has infinite support without being a fixed-point-free involution, then any $ s \in S$ is a product of three conjugates of $ p$. Furthermore, we present uncountably many new conjugacy classes $ C$ of $ S$ satisfying that any $ s \in S$ is a product of two elements of $ C$. Similar results are shown for permutations of uncountable sets.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0773066-3
Keywords: Infinite symmetric groups, finite symmetric groups, alternating groups, permutations, conjugacy classes, involutions, orbits, fixed points
Article copyright: © Copyright 1985 American Mathematical Society

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