Cubes of Conjugacy Classes Covering the Infinite Symmetric Group
نویسنده
چکیده
Using combinatorial methods, we prove the following theorem on the group S of all permutations of a countably-infmite set: Whenever p 6 S has infinite support without being a fixed-point-free involution, then any s G S is a product of three conjugates of p. Furthermore, we present uncountably many new conjugacy classes C of S satisfying that any s G S is a product of two elements of C. Similar results are shown for permutations of uncountable sets.
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