Are there any interesting subsets of elementary abelian 2-groups studied in the literature? What properties do they have?
Interesting subgroups of elementary abelian 2-groups
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$\begingroup$
group-theory
1 Answers
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"Interesting"? Such a subjective thing...Anyway: any elementary 2-group can be seen as a vector space over the field $\,\,\mathbb{F}_2:=\mathbb{Z}/2\mathbb{Z}\,\,$ , and its subgroups are precisely this vector space's subspaces, so...well, if you know a little linear algebra and you're interested in it perhaps this will appeal you.
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5Many of the most popular error-correcting codes are vector spaces over the field of 2 elements, so that might be a good place to start looking for interesting subgroups with well-studied properties. – 2012-05-29