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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Squares of conjugacy classes in the infinite symmetric groups


Author: Manfred Droste
Journal: Trans. Amer. Math. Soc. 303 (1987), 503-515
MSC: Primary 20B30; Secondary 20E32
MathSciNet review: 902781
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Abstract: Using combinatorial methods, we will examine squares of conjugacy classes in the symmetric groups $ {S_\nu }$ of all permutations of an infinite set of cardinality $ {\aleph _\nu }$. For arbitrary permutations $ p \in {S_\nu }$, we will characterize when each element $ s \in {S_\nu }$ with finite support can be written as a product of two conjugates of $ p$, and if $ p$ has infinitely many fixed points, we determine when all elements of $ {S_\nu }$ are products of two conjugates of $ p$. Classical group-theoretical theorems are obtained from similar results.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0902781-5
Keywords: Infinite symmetric groups, finite symmetric groups, permutations, conjugacy classes, orbits, fixed points
Article copyright: © Copyright 1987 American Mathematical Society