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

**Classical groups**

**Finite groups**

**Group schemes**

**Topological groups**

**Lie groups**

**Super-Lie groups**

**Higher groups**

**Cohomology and Extensions**

**Related concepts**

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 $p = 2$ and hence also often denoted $C_2$.

In the ADE-classification of finite subgroups of SU(2), the group of order 2 is the smallest non-trivial group, and the smallest in the A-series:

**ADE classification** and **McKay correspondence**

Last revised on May 22, 2023 at 18:40:09. See the history of this page for a list of all contributions to it.