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Let G be the group
the set of binary vectors in which ai=0 or 1Let 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)
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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.
"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..."
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