Endomorphism structure of groups of order 1

This article gives specific information, namely, endomorphism structure, about a family of groups, namely: groups of order 1.
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The only group of order 1 is the trivial group, so this page discusses the endomorphism structure of the trivial group.

Automorphism group

The automorphism group of the trivial group is the trivial group. Indeed, the only map from the trivial group to itself is the map sending the identity element to itself, which is an automorphism.

(The only two groups to have the trivial group as its automorphism group is the trivial group and cyclic group:Z2.)