Twisted subgroup

This article defines a property of subsets of groups
View other properties of subsets of groups|View properties of subsets of abelian groups|View subgroup properties

Definition

Definition with symbols

A subset $K$ of a group $G$ is termed a twisted subgroup if it satisfies the following two conditions:

• The identity element belongs to $K$
• Given $x,y$ in $K$, the element $xyx$ is in $K$

Property theory

Associates

Let $K$ be a twisted subgroup of $G$. Then, for any $a$ in $K$, the sets $Ka$ and $a^{-1}K$ are equal and form another twisted subgroup. Such a twisted subgroup is termed an associate of $K$. The relation of being associate is an equivalence relation and we are interested in studying twisted subgroups upto the equivalence relation of being associates.

Intersection

The intersection of a subgroup and a twisted subgroup is a twisted subgroup.

References

PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

One of the people editing this page intended to fill in this information at a later stage, but hasn't gotten around to doing it yet. If you see this placeholder for a long time, file an error report at the error reporting page.

from Foguel's article

External links

• Tuval Foguel's list of publications which include publications on twisted subgroups