Vol. 8, No. 5, 2015

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
On the cardinality of infinite symmetric groups

Matt Getzen

Vol. 8 (2015), No. 5, 749–751
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.

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

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