Ivan Shishkin, Birch Grove

Group

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Revision 5258

9/17/2026, 2:23:23 PM · SalixBabylonica

Added exercise "Quelques propriétés d'un groupe"

linked exercisesElément neutre du groupe des entiers relatifs, Des exemples de groupes ?Elément neutre du groupe des entiers relatifs, Des exemples de groupes ?, Quelques propriétés d’un groupe

Revision 4633

9/12/2026, 9:50:50 AM · Ancient Tree

Added exercise "Des exemples de groupes ?"

linked exercisesElément neutre du groupe des entiers relatifsElément neutre du groupe des entiers relatifs, Des exemples de groupes ?

Revision 4629

9/12/2026, 9:43:48 AM · Ancient Tree

Added exercise "Elément neutre du groupe des entiers relatifs"

linked exercisesNoneElément neutre du groupe des entiers relatifs

Revision 816

8/1/2026, 5:44:12 PM · Sequoia

Concept edited

Compare with revision 2452 changed lines
1A group is a [[Set|set]] $G$ equipped with a [[Binary operation|binary operation]] $*:G\times G \rightarrow G$ satisfying the following properties :
1A group is a [[Set|set]] $G$ equipped with a [[Operation|binary operation]] $*:G\times G \rightarrow G$ satisfying the following properties :
21) Associativity : for all $a,b,c\in G$, $(a*b)*c=a*(b*c)$.
32) Identity element : there exists an element $e\in G$ such that $e*a=a*e=a$ for every $a\in G$.
43) Inverses : for every $a\in G$, there exists an element $a^{-1}\in G$ such that $a*a^{-1}=a^{-1}*a=e$.
5
6##### Remarks
7- When the context is clear, the operation $*$ is often ommited, writing $ab$ for $a*b$.

Revision 245

7/7/2026, 8:54:01 AM · Ancient Tree

Concept edited

This older revision predates detailed metadata tracking.

Revision 240

7/7/2026, 8:46:00 AM · Ancient Tree

Concept edited

Compare with revision 2393 changed lines
1A group is a [[Set|set]] $G$ equipped with a [[Binary operation|binary operation]] $*:G\times G \rightarrow G$ satisfying the following properties :
21) Associativity : for all $a,b,c\in G$, $(a*b)*c=a*(b*c)$.
32) Identity element : there exists an element $e\in G$ such that $e*a=a*e=a$ for every $a\in G$.
43) Inverses : for every $a\in G$, there exists an element $a^{-1}\in G$ such that $a*a^{-1}=a^{-1}*a=e$.
5
6##### Remarks
7- When the context is clear, the operation $*$ is often ommited, writing $ab$ for $a*b$.

Revision 239

7/7/2026, 8:42:06 AM · Ancient Tree

Concept edited

Compare with revision 1095 changed lines
1A group is...
1A group is a [[Set|set]] $G$ equipped with a [[Binary operation|binary operation]] $*:G\times G \rightarrow G$ satisfying the following properties :
21) Associativity : for all $a,b,c\in G$, $(a*b)*c=a*(b*c)$.
32) Identity element : there exists an element $e\in G$ such that $e*a=a*e=a$ for every $a\in G$.
43) Inverses : for every $a\in G$, there exists an element $a^{-1}\in G$ such that $a*a^{-1}=a^{-1}*a=e$.

Revision 109

6/27/2026, 8:24:10 AM · Ancient Tree

Concept created

A group is...