group theory

# Contents

## Definition

There is, up to isomorphism, a unique simple group of order 2:

it has two elements $\left(1,\sigma \right)$, where $sigm\cdot \sigma =1$.

This is usually denoted ${ℤ}_{2}$ or $ℤ/2ℤ$, because it is the cokernel (the quotient by the image of) the homomorphism

$\cdot 2:ℤ\to ℤ$\cdot 2 : \mathbb{Z} \to \mathbb{Z}

on the additive group of integers. As such ${ℤ}_{2}$ is the special case of a cyclic group ${ℤ}_{p}$ for $p=2$.

Revised on October 17, 2012 13:05:06 by Urs Schreiber (82.169.65.155)