# 2-powered twisted subgroup

From Groupprops

## Definition

A subset of a group is termed a **2-powered twisted subgroup** if it satisfies **both** the following conditions:

- For every , there exists a
*unique*element such that . - is a twisted subgroup of , i.e., it contains the identity element, is closed under taking inverses, and for every , we have .

## Particular cases

- We can restrict the twisted multiplication on a 2-powered group to any 2-powered twisted subgroup.
- 2-powered twisted subgroups in Baer Lie groups are in correspondence with 2-powered subgroups of the additive group of the Lie ring under the Baer correspondence.