MathLiveLagrange's theorem
For a finite group G and a subgroup H, the order of G equals the index of H in G multiplied by the order of H. It implies that the order of any subgroup divides the order of the group.
|G| = [G:H] \cdot |H|What the symbols mean
| order (number of elements) of the finite group G | |
| index of the subgroup H in G, the number of left cosets of H in G | |
| order (number of elements) of the subgroup H |
About this formula
- FieldMathematics
- TopicGroup theory
- LevelUniversity
- Also calledorder of subgroup divides group order, index of subgroup formula, group order subgroup index, Lagrange theorem group theory, order of group equals index times subgroup order
- SourceWikidata Q505798
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