# Inverse Conjugacies and Reversing Symmetry Groups

Let $$G$$ be a group and $$C(a)$$ be the centralizer of $$a\in G$$.  The author studies the properties of the skew centralizer $$B(a)=\{x\in G : xa=a^{-1}x \}$$ and the reversing symmetry group $$E(a)=B(a)\cup C(a)$$ of $$a$$.  Many properties provide nice exercises for an introductive course of abstract algebra.  The author also shows the dynamical origin and applications of such algebraic structures, which arise naturally from the ergodic theory of measure-preserving transformations.

Author(s):
Geoffrey R. Goodson
Publication Date:
Wednesday, June 11, 2014
Original Publication Source:
American Mathematical Monthly
Original Publication Date:
January, 1999
Subject(s):
Algebra and Number Theory
Abstract Algebra
Groups
Differential & Difference Equations
Dynamical Systems
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Applicable Course(s):
4.2 Mod Algebra I & II
Modify Date:
Wednesday, June 11, 2014