Math and science::Algebra::Aluffi

Group. Definition.

A group is a [something with a what?].

More specifically, a group is the set [of what of a something].

Recall that a groupoid is a category where every morphism is an isomorphism.

Now the usual approach.

A group $(G, ∙)$ is a set $G$ and a function $∙ : G \times G \to G$ (called a binary operation) where the following three properties are satisfied:

Associativity: $∙$ is associative,

[ $?$ ]
Identity: There exists an identity element denoted $e_{G}$ for $∙$ ,

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Inverse: Every element of $G$ has an inverse with respect to $∙$ ,

[ $?$ ]

08.11.2020