The order of a group $(G,\ast)$ is the cardinality of the set $G.$ It is denoted by $|G|.$ We call $G$ a finite group, if $|G|$ is finite. Otherwise we call $G$ an infinite group.
Explanations: 1
Proofs: 2 3 4 5
Propositions: 6
Theorems: 7 8 9 10