## A Conversation for Group Theory

### Legrange's Theorem

LQ - Just plain old LQ Started conversation Sep 23, 2006

An excellent entry; interesting and (mostly) easily followed - although it may help I've done some of it before.

One thing though - you mention Legrange's Theorem, but don't actually say what it is, merely a consequence of it. Is that consequence the only thing in the theorem? Or is the theorem too complex to try and describe in an article like this?

Great to see maths being covered in the Guide, anyway!

### Legrange's Theorem

Silverfish Posted Sep 29, 2006

I'm glad you like the entry.

As for langrange's theorem, there seems to be some disagreement about what exactly Langrange's theorem consists of. Some sources say it is actually the statement that if G is a finite group, then the order of any subgroups H divides the order of G.

However, mathworld (see the entry here: http://mathworld.wolfram.com/LagrangesGroupTheorem.html) states that "The most general form of Lagrange's theorem", is a more general statement, from which the statement above is a consequence. That was probably the entry I was using as a guide.

That definition isn't drastically more complicates, but it would mean I had to mention cosets and indices, and in any case, it's only the bit about subgroups having orders dividing the order of the main group, that I actually use later on.

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