Dihedral trick
From Groupprops
This fact is useful in work leading up to the Classification of finite simple groups
This article describes a method that can be used to prove that two elements inside a group are conjugate
Contents
Statement
Statement with symbols
Let and be two distinct involutions (elements of order two) in a finite group . Suppose has order . Then, is a dihedral group of order , with cyclic subgroup of order generated by and the element of order two conjugating to its inverse.
Related facts
Applications
References
Textbook references
- Finite Groups by Daniel Gorenstein, ISBN 0821843427, Page 301, Theorem 1.1, Chapter 9 (Groups of even order), Section 1 (Elementary properties of involutions), ^{More info}