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
DOI:
https://doi.org/10.1090/S0002-9947-1987-0902781-5
MathSciNet review:
902781
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Using combinatorial methods, we will examine squares of conjugacy classes in the symmetric groups of all permutations of an infinite set of cardinality
. For arbitrary permutations
, we will characterize when each element
with finite support can be written as a product of two conjugates of
, and if
has infinitely many fixed points, we determine when all elements of
are products of two conjugates of
. Classical group-theoretical theorems are obtained from similar results.
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Additional Information
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