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can we use Lazard Correspondence for p-groups of maximal class and why?

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You can use the Lazard correspondence on any $p$-group of class less than $p$. So, in particular, you can also use it on $p$-groups of maximal class, as long as $p$ is larger than the class. This is useful for "asymptotic" statements, but if you are interested in results for a fixed $p$, or for all $p$, then you will have to bound the order $p^n$ of your group quite severely. –  Max Horn Apr 5 '12 at 10:28
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Your question could be improved if you follow some of the advice on the "how to ask" page, linked at the top of this one. –  S. Carnahan Apr 6 '12 at 7:18
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