Definition:Self-Inverse Element/Definition 1
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Definition
Let $\struct {S, \circ}$ be a monoid whose identity element is $e_S$.
Let $x \in S$ be an element of $S$.
$x$ is a self-inverse element of $\struct {S, \circ}$ if and only if $x \circ x = e_S$.
Also known as
The definition of a self-inverse element is usually made in the context of a group.
Some sources refer to such an element as an involution.
Also see
Sources
- 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $1$: Introduction to Finite Group Theory: $1.13$