Involve: A Journal of Mathematics

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

On the cardinality of infinite symmetric groups

Matt Getzen

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

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

References

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