group of order 2

- group, ∞-group
- group object, group object in an (∞,1)-category
- abelian group, spectrum
- group action, ∞-action
- representation, ∞-representation
- progroup
- homogeneous space

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

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

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

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

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

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