E-automorphism

Definition with symbols
An automorphism $$\sigma$$ of a group $$G$$ is termed an e-automorphism if given any $$\sigma$$-invariant subgroups $$A < B$$, there exists an element $$x \in B \setminus A$$ such that $$x^{-1}\sigma(x) \in A$$.

Relation with other properties

 * Algebraic automorphism: It is conjectured that every e-automorphism is algebraic.