Lagrange's Theorem | Mathematics | Page 1

charred stone Jul 20, 2023, 2:08 PM

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How can you prove this theorem?

soft baneBOT Jul 20, 2023, 2:08 PM

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devout crown Jul 20, 2023, 2:28 PM

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charred stone How can you prove this theorem?

https://en.m.wikipedia.org/wiki/Lagrange's_theorem_(group_theory)

Lagrange's theorem (group theory)

In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of every subgroup of G divides the order of G. The theorem is named after Joseph-Louis Lagrange. The following variant states that for a subgroup

H
H

of a finite group

G
G

...

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Read up on the proof. If it's too complicated, I recommend reading any undergraduate textbook on group theory. Lagrange's Theorem is pretty much always proved since the proof is easy to explain.

#Lagrange's Theorem