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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cubes of conjugacy classes covering the infinite symmetric group
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by Manfred Droste PDF
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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Additional 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