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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For a finite group
For a periodic group
An automorphism of a periodic group is termed a cofactorial automorphism for if every prime dividing the order of equals the order of some non-identity element of .
For a group with elements of infinite order
If the group has any element of infinite order, then every automorphism of the group is considered to be a cofactorial automorphism.