Cubes of conjugacy classes covering the infinite symmetric group
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- by Manfred Droste
- Trans. Amer. Math. Soc. 288 (1985), 381-393
- DOI: https://doi.org/10.1090/S0002-9947-1985-0773066-3
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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.References
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Bibliographic Information
- © Copyright 1985 American Mathematical Society
- 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