group of order 2



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 and hence also often denoted C 2C_2.

Revised on January 22, 2016 15:05:32 by Urs Schreiber (