Artículos de revistas
Finiteness Conditions On Subgroups Of Profinite P-poincaré Duality Groups
Registro en:
Israel Journal Of Mathematics. , v. 173, n. 1, p. 367 - 377, 2009.
212172
10.1007/s11856-009-0096-8
2-s2.0-71249147989
Autor
Kochloukova D.H.
Pinto A.G.S.
Institución
Resumen
For a prime number p let G be a profinite p-PDn group with a closed normal subgroup N such that G/N is a profinite p-PDm group and that Hi(V,Fp) is finite for every open subgroup V of N and all i ≤ [n/2]. Generalising [12, Thm. 3. 7. 4] we show that m ≤ n and N is a profinite p-PDn - m group. In case that G is a pro-pPDn group of Euler characteristic 0 with a closed normal subgroup N of type FP[n-1 / 2] such that G/N is soluble-by-finite pro-p group of finite rank, we show that N is a pro-pPDn-m group, where m = vcdp(G/N). As a corollary we obtain that a pro-pPD3 group with infinite abelianization is either soluble or contains a free nonprocyclic pro-p subgroup. © Hebrew University Magnes Press 2009. 173 1 367 377 Demushkin, S., On the maximal p-extension of a local field (1961) Izvestiya Akademii Nauk USSR Seriya Matematicheskaya, 25, pp. 329-346 Demushkin, S., On 2-extensions of a local field (1963) Sibirski'i Matematiceski'i Zhurnal, 4, pp. 951-955 Dixon, J.D., du Sautoy, M.P.F., Mann, A., Segal, D., (1991) Analytic Pro-P Groups, 157. , London Mathematical Society Lecture Notes Series, Cambridge: Cambridge University Press Evans, B., Moser, L., Solvable fundamental groups of compact 3-manifolds (1972) Transactions of the American Mathematical Society, 168, pp. 189-210 Gelfand, S.I., Manin Yu., I., (1988) Methods in Homological Algebra, Vol. 1, Introduction to the Theory of Cohomology and Derived Categories, , Moscow: Nauka King, J.D., Homological finiteness conditions for pro-p groups (1999) Communications in Algebra, 27, pp. 4969-4991 Hillman, J., Kochloukova, D., Finiteness conditions and PDr-group covers of PDn-complexes (2007) Mathematische Zeitschrift, 256, pp. 45-56 Kochloukova, D.H., On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version (2006) Journal of Pure and Applied Algebra, 204, pp. 536-554 Kochloukova, D., Zalesskii, P., Tits alternative for 3-manifold groups (2007) Archiv der Mathematik, 88, pp. 364-367 Labute, J.P., Classification of Demushkin groups (1967) Canadian Journal of Mathematics, 19, pp. 106-132 Lazard, M., Groups analytiques p-adiques (1965) Institut des Hautes Études Scientifiques Publications, 26, pp. 389-603 Neukirch, J., Schmidt, A., Wingberg, K., (2000) Cohomology of Number Fields, , Berlin: Springer-Verlag Ribes, L., Zalesskii, P., (2000) Profinite Groups, , Berlin: Springer-Verlag Serre, J.-P., (1997) Galois Cohomology, , Berlin: Springer-Verlag Serre, J.-P., Structure of certain pro-p group (after Demushkin) (1995) Séminaire Bourbaki, 8, pp. 145-155. , Paris: Exp. N252, Soc. Math. France Symonds, P., Weigel, T., Cohomology of p-adic analytic groups (2000) New Horizons in Pro-P Groups, 184, pp. 349-410. , Progress in Mathematics, Boston, MA: Birkhäuser Boston Weibel, C.A., (1994) An Introduction to Homological Algebra, 38. , Cambridge Studies in Advanced Mathematics, Cambridge: Cambridge University Press Wilson, J., (1998) Profinite Groups, 19. , London Mathematical Society Monographs. New Series, New York: The Clarendon Press Oxford University Press Zelmanov, E., On groups satisfying the Golod-Shafarevich condition, in New horizons in pro-p groups (2000) Progress in Mathematics, pp. 223-232. , Boston, MA: Birkhäuser Boston