Rewriteability in Finite Groups

Authors

Judy Leavitt Walker, University of Nebraska - LincolnFollow
G. J. Sherman, Rose-Hulman Institute of Technology
Mark E. Walker, University of Nebraska - LincolnFollow

Document Type

Article

Date of this Version

1992

Citation

From: The American Mathematical Monthly, Vol. 99, No. 5 (May, 1992), pp. 446-452. doi 10.1080/00029890.1992.11995873

Comments

Published by Taylor & Francis, Ltd. on behalf of the Mathematical Association of America.

Abstract

What's the probability that two elements in a finite group commute? A formal answer,

Pr₂(G) = {(x, y) [element of] G² |xy = yx}| / |G|²

begs our next question. How many ordered pairs of elements of a finite group commute?