Why is Lagrange's theorem so important? Sure, |H| divides |G|. but why is this important? I dont seem to get why it is.

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- Oct 26th 2009, 03:42 PMsfspitfire23what can Lagrange do?
Why is Lagrange's theorem so important? Sure, |H| divides |G|. but why is this important? I dont seem to get why it is.

- Oct 26th 2009, 04:13 PMtonio

Well, I think Lagrange can do squat since he's been dead, but this theorem of his is VERY important in finite group theory since, to begin with,it gives a very nice and easy-to-check test to rule out possible subgroups of groups. For example, a group of order 10 can only have proper subgroups of order 2 and 5 (besides the trivial one), and that already rules out 7 possible orders.

You have to wait until you advance a little more in your group theory studies to begin to realize how basic and important this result is.

Tonio