Vol. 8, No. 5, 2015

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On the cardinality of infinite symmetric groups

Matt Getzen

Vol. 8 (2015), No. 5, 749–751

A new proof is given that the symmetric group of any set X with three or more elements, finite or infinite, has cardinality strictly greater than that of X. Use of the axiom of choice is avoided throughout.

set theory, infinite symmetric groups, axiom of choice
Mathematical Subject Classification 2010
Primary: 03E99
Secondary: 20B30, 03E25
Received: 7 January 2014
Accepted: 12 July 2014
Published: 28 September 2015

Communicated by Kenneth S. Berenhaut
Matt Getzen
Department of Mathematics & Computer Science
Arcadia University
450 South Easton Road
Glenside, PA 19038
United States