Lagrange's theorem (group theory)

Theorem on the orders of subgroups

In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is a divisor of | G | {\displaystyle |G|} . That is, the order (number of elements) of every subgroup divides the order of the whole group. The theorem is named after Joseph-Louis Lagrange.

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