# Group Theory- Zassenhaus Filtration & Other Filtrations

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 !

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## 1 Answer

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.

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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