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.