Lagrange's theorem (group theory)
Theorem on the orders of subgroups
Lagrange's theorem (group theory)
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. The following variant states that for a subgroup H {\displaystyle H} of a finite group G {\displaystyle G} , not only is | G | / | H | {\displaystyle |G|/|H|} an integer, but its value...
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