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ROBBYM

Member

Registered: 2008-04-24

Posts: 10

Group theory - lagranges theorem

Let G be the group

the set of binary vectors

in which ai=0 or 1

Let H be the subset of G consisting of all binary vectors with an even number of 1's. show that H is a subgroup of G.

Determine the order of H

please help me with this question i've had a look at proofs of lagranges theorem but i dont really see how i can possibly apply it to this question.

Last edited by ROBBYM (2008-04-24 21:28:11)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Group theory - lagranges theorem

The only way I see Lagrange helping you is to determine the size of H.  You know that |H| | |G|, which means that H must be a power of 2 as well.

However, Lagrange will do nothing for you in proving that it is an actual subgroup.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."