E-automorphism

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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Definition

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.