A group $(G,\ast)$ is a monoid, in which an inverse element exists for each element, i.e. for all $x\in G$ there is an $x^{-1}\in G$ with $x\ast x^{-1} =x^{-1}\ast x=e,$ where $e\in G$ is the neutral element.
Please note that $e\in X$ is unique in $G$ and $x^{-1}$ is unique for all $x\in G.$
Axioms: 1
Branches: 2
Chapters: 3 4 5
Corollaries: 6
Definitions: 7 8 9 10 11 12 13 14 15 16 17 18
Examples: 19 20
Explanations: 21 22
Lemmas: 23 24 25
Motivations: 26
Problems: 27 28
Proofs: 29 30 31 32 33 34 35 36 37 38 39 40 41 42
Propositions: 43 44 45 46 47 48 49 50 51
Solutions: 52
Theorems: 53 54 55
