Analyticity and Growth of Pro-p-Groups
- 141 Downloads
Our subject are the algebraic properties of p-adic analytic groups. We present first the theory of finite and pro-finite powerful p-groups, as developed by Lubotzky and Mann. Then we show, following work by Lubotzky, Mann and Segal, how this theory, and previous results of Lubotzky characterizing linear groups, can be applied to the study of residually finite groups of finite (Prüfer) rank. Finally, we present some recent work of Lubotzky, Mann, Segal and Du Sautoy related to polynomial subgroup growth.
KeywordsNormal Subgroup Sylow Subgroup Finite Index Finite Rank Open Subgroup
Unable to display preview. Download preview PDF.
-  W. M. Kantor and A. Lubotzky, The probability of generating a finite classical group, to appear in Geom. Ded.Google Scholar
- A. Lubotzky and A. Mann, On groups of polynomial subgroup growth, to appear in Invent. math.Google Scholar
- A. Mann and D. Segal, Uniform finiteness conditions in residually finite groups, to appear in Proc. Camb. Phil. Soc.Google Scholar
- D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups. (Part 1 and 2) Springer, Berlin, 1972.Google Scholar
- D. Segal, Subgroups of finite index in soluble groups. In: Groups, St. Andrews 1985, Ed. C. M. Campbell, E. E. Robertson, pp. 307–319, Cambridge University Press, Cambridge, 1986.Google Scholar
- S. S. Shatz, Profinite Groups, Arithmetic, and Geometry. Princeton, 1972.Google Scholar
- B. A. F. Wehrfritz, Infinite Linear Groups. Springer, Berlin, 1967.Google Scholar