Involve: A Journal of Mathematics

  • Involve
  • Volume 8, Number 5 (2015), 749-751.

On the cardinality of infinite symmetric groups

Matt Getzen

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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.

Article information

Involve, Volume 8, Number 5 (2015), 749-751.

Received: 7 January 2014
Accepted: 12 July 2014
First available in Project Euclid: 22 November 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E99: None of the above, but in this section
Secondary: 20B30: Symmetric groups 03E25: Axiom of choice and related propositions

set theory infinite symmetric groups axiom of choice


Getzen, Matt. On the cardinality of infinite symmetric groups. Involve 8 (2015), no. 5, 749--751. doi:10.2140/involve.2015.8.749.

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  • J. W. Dawson, Jr. and P. E. Howard, “Factorials of infinite cardinals”, Fund. Math. 93:3 (1976), 185–195.