nLab
group of order 2

Contents

Definition

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

it has two elements (1,σ)(1,\sigma), where σσ=1\sigma \cdot \sigma = 1.

This is usually denoted 2\mathbb{Z}_2 or /2\mathbb{Z}/2\mathbb{Z}, because it is the cokernel (the quotient by the image of) the homomorphism

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

on the additive group of integers. As such 2\mathbb{Z}_2 is the special case of a cyclic group p\mathbb{Z}_p for p=2p = 2.

Revised on September 30, 2013 14:03:17 by Anonymous Coward (77.177.112.121)