Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Does someone know of any good papers/books/references of properties of the so-called "Zassenhaus Filtration" of a group $G$ ?

I'm mainly interested in relations between this filtration and closely related ones such as the lower central series (which I actually already found ) , the derived series, etc...

Any good reference will be greatfully acknowledged! I really need to know some properties of this filtration, but can't find any good book/paper that contains such

Thanks in advance !

share|improve this question
add comment

1 Answer 1

up vote 1 down vote accepted

For a survey and applications of Zassenhaus filtration see this recent survey by Misha Ershov. For a "canonical" text see J. D. Dixon, M. P. F. du Sautoy, A. Mann and D. Segal, Analytic pro-p groups. Second edition. Cambridge Studies in Advanced Mathematics, 61. Cambridge University Press, Cambridge, 1999.

share|improve this answer
    
Thanks a lot Mark Sapir! Have you got any idea if one of these references contains some relation between the derived series and the Zass. Filtration? –  jason mfash Jun 21 '12 at 20:09
    
One is inside another by definition (or I do not understand your question). –  Mark Sapir Jun 21 '12 at 20:52
    
So what you're actually saying is that the derived series is contained in the zassenhaus filtration ? What about any results about bounding the other direction ? (something like - the n'th term of the zass. filtration is contained in the 10000n's term of the derived series)? Have you got any idea? Thanks a lot again ! –  jason mfash Jun 22 '12 at 6:42
    
@Jason: Take a cyclic group of order $p^{10000}$. Compare its Z. filtration with the lower central series and the derived series. –  Mark Sapir Jun 22 '12 at 8:04
add comment

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.