Endomorphism structure of cyclic group:Z2

This article gives specific information, namely, endomorphism structure, about a particular group, namely: cyclic group:Z2.
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This article is about the structure of endomorphisms of cyclic group:Z2 (GAP ID: (2,1)) which we will take as having the following presentation:

$\langle g\mid g^{2}=e\rangle$

where $e$ denotes the identity element.

Summary of information

Construct	Value	Order	Second part of GAP ID (if group)	Comment
automorphism group	trivial group	1	1
inner automorphism group	trivial group	1	1
outer automorphism group	trivial group	1	1

Description of automorphism group

The only two possible bijections from the group to itself are the maps $e\mapsto e$, $g\mapsto g$ (the identity map) and $e\mapsto g$, $g\mapsto e$. The second one is not an automorphism since, for example, the orders of the elements are not preserved. Thus, the automorphism group is a group of order 1, isomorphic to the trivial group.