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Group whose automorphism group is transitive on non-identity elements
From Groupprops
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Definition
Symbol-free definition
A group whose automorphism group is transitive on non-identity elements is a group with the property that given any two non-identity elements of the group, there exists an automorphism of the group sending the first to the second.
Definition with symbols
Let G be a group. Then we say that the automorphism group of G is transitive on non-identity elements if, given any two non-identity elements 
, there exists 
such that σ(g) = h.
Note that for an Abelian group, this is equivalent to the property of being the additive group of a field.
Relation with other properties
Stronger properties
Weaker properties
Facts about Group whose automorphism group is transitive on non-identity elementsRDF feed
| Stronger than | Characteristically simple group + |
| Weaker than | Additive group of a field +, and Group with two conjugacy classes + |
