Abstract
In this paper we establish the existence of profinite Frobenius subgroups in a free prosolvable productA ∐B of two finite groupsA andB. In this way the classification of solvable subgroups of free profinite groups is completed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Binz, E., Neukirch, J., Wenzel, G. H.: A subgroup theorem for free products of profinite groups. J of Algebra19, 104–109 (1971).
Gildenhuys, D., Herfort, W., Ribes, L.: Profinite Frobenius groups. Arch. Math.33, 518–528 (1979).
Gildenhuys, D., Ribes, L.: A Kurosh subgroup theorem for free pro-C-products of pro-C-groups. Trans. Amer. Math. Soc.186, 309–329 (1973).
Haran, D.: On closed subgroups of free products of profinite groups. J. London Math. Soc. (3)55, 266–298 (1987).
Haran, D., Lubotzky, A.: Maximal abelian subgroups of free profinite groups. Math. Proc. Camb. Phil. Soc.97, 51–55 (1985).
Herfort, W., Ribes, L.: Torsion elements and centralizers in free products of profinite groups. J. Reine Angew. Math.358, 155–325 (1985).
Herfort, W., Ribes, L.: Subgroups of free pro-p-products. Math. Proc. Camb. Phil. Soc.101, 197–206 (1987).
Herfort, W., Ribes, L.: Solvable subgroups of free products of profinite groups. Proc. Singapore Group Theory Conf. 1987. W. de Gruyter. To appear.
Huppert, B.: Endliche Gruppen. Berlin-Heidelberg-New York: Springer. 1967.
Kelly, J. L.: General Topology. New York: D. Van Nostrand. 1955.
Magnus, W., Karrass, A., Solitar, D.: Combinatorial Group Theory. Interscience 1966.
Mel'nikov, O. V.: Normal subgroups of free profinite groups. Math. USSR Izvestija12, 1–20 (1978).
Mel'nikov, O. V.: Subgroups and homology of free products of profinite groups (in Russian). AN BSSR, Preprint 20 (290), Minsk 1987.
Neukirch, J.: Freie Produkte pro-endlicher Gruppen und ihre Kohomologie. Arch. Math.22, 337–357 (1971).
Ribes, L.: Introduction to profinite groups and Galois cohomology. Queen's Papers Pure Appl. Math.,24, Kingston (1970).
Ribes, L.: The Cartesian subgroup of a free product of profinite groups. To appear.
Scott, W. R.: Group Theory. New Jersey: Prentice Hall 1965.
Serre, J.-P.: A Course in Arithmetic. Berlin-Heidelberg-New York: Springer. 1973.
Serre, J.-P.: Cohomologie Galoisienne. Lecture Notes Math.5. Berlin-Heidelberg-New York: Springer 1965.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Herfort, W.N., Ribes, L. Frobenius subgroups of free products of prosolvable groups. Monatshefte für Mathematik 108, 165–182 (1989). https://doi.org/10.1007/BF01308669
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01308669