Cubes of conjugacy classes covering the infinite symmetric group

Droste, Manfred

doi:10.1090/S0002-9947-1985-0773066-3

Cubes of conjugacy classes covering the infinite symmetric group
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Trans. Amer. Math. Soc. 288 (1985), 381-393 Request permission

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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