order of products

If a and b are elements of a group, then both ab and ba have always the same order.

Proof.  Let e be the indentity element of the group.  For  n>1,  we have the equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath (http://planetmath.org/Equivalent3) conditions


As for the infinite order, it makes the conditions false.

Note.  More generally, all elements of any conjugacy classMathworldPlanetmathPlanetmath have the same order.

Title order of products
Canonical name OrderOfProducts
Date of creation 2013-03-22 18:56:43
Last modified on 2013-03-22 18:56:43
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Theorem
Classification msc 20A05
Related topic InverseFormingInProportionToGroupOperation