Definition: Group Order

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


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References

Bibliography

  1. Fischer, Gerd: "Lehrbuch der Algebra", Springer Spektrum, 2017, 4th Edition