Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

A Crystallographic Group is a discrete group of isometries acting on the n-dimensional euclidean space $\mathbb{R} ^n $ with compact fundamental domain.

A lattice is a crystallographic group which consists only of translations.

We have a theorem that says that every crystallographic group contains n linearly independent translations.

Now, we take $L$ to be the subgroup of an n-dimensional crystallographic group $G$ consisting of all pure translations in G.

Does the first theorem I stated implies $L$ must be a lattice?

Thanks a lot !

share|cite|improve this question
What is a "pure translation"? – rschwieb May 21 '12 at 16:41
Is a pure translation is a translation, that looks like a tautology to me. Except that you must show that $n$ independent translations in dimension $n$ imply compact fundamental domain, but that is true as well. – Marc van Leeuwen May 21 '12 at 16:51

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.