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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511370945

Digital Object Identifier
doi:10.2140/involve.2015.8.749

Mathematical Reviews number (MathSciNet)
MR3404654

Zentralblatt MATH identifier
1325.03055

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

Keywords
set theory infinite symmetric groups axiom of choice

Citation

Getzen, Matt. On the cardinality of infinite symmetric groups. Involve 8 (2015), no. 5, 749--751. doi:10.2140/involve.2015.8.749. https://projecteuclid.org/euclid.involve/1511370945


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References

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