Sharply transitive linear groups over algebraically closed fields
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- by Gregory Cherlin, Theo Grundhöfer, Ali Nesin and Helmut Völklein PDF
- Proc. Amer. Math. Soc. 111 (1991), 541-550 Request permission
Abstract:
We classify the groups from the title. The result is interpreted in terms of nearfields, and applied to a problem in the model theory of permutation groups.References
- Yvette Amice, Les nombres $p$-adiques, Collection SUP: “Le Mathématicien”, vol. 14, Presses Universitaires de France, Paris, 1975 (French). Préface de Ch. Pisot. MR 0447195
- Friedrich Bachmann, Aufbau der Geometrie aus dem Spiegelungsbegriff, Die Grundlehren der mathematischen Wissenschaften, Band XCVI, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959 (German). MR 0107835
- Gregory Cherlin, Superstable division rings, Logic Colloquium ’77 (Proc. Conf., Wrocław, 1977) Studies in Logic and the Foundations of Mathematics, vol. 96, North-Holland, Amsterdam-New York, 1978, pp. 99–111. MR 519805
- Ulrich Felgner, Pseudofinite near-fields, Near-rings and near-fields (Tübingen, 1985) North-Holland Math. Stud., vol. 137, North-Holland, Amsterdam, 1987, pp. 15–29. MR 890752, DOI 10.1016/S0304-0208(08)72282-5
- Nathan Jacobson, Basic algebra. II, 2nd ed., W. H. Freeman and Company, New York, 1989. MR 1009787
- Franz Kalscheuer, Die Bestimmung aller stetigen Fastkörper über dem Körper der reellen Zahlen als Grundkörper, Abh. Math. Sem. Hansischen Univ. 13 (1940), 413–435 (German). MR 1968 W. Kerby, On infinite sharply transitive multiply transitive groups, Hamburger Mathematische Einzelschriften, 1974.
- Ali Nesin, On sharply $n$-transitive superstable groups, J. Pure Appl. Algebra 69 (1990), no. 1, 73–88. MR 1082446, DOI 10.1016/0022-4049(90)90079-W
- Ali Nesin, Nonsolvable groups of Morley rank $3$, J. Algebra 124 (1989), no. 1, 199–218. MR 1005703, DOI 10.1016/0021-8693(89)90159-2
- Klaus Schulz, Undecidability of the theory of finite nearfields, Results Math. 14 (1988), no. 3-4, 340–348. MR 964050, DOI 10.1007/BF03323236 H. Zassenhaus, Über endliche Fastkörper, Abh. Math. Sem. Hamb. Univ. 11 (1936), 187-220.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 541-550
- MSC: Primary 20A15; Secondary 03C45, 03C60, 20B22, 20H20
- DOI: https://doi.org/10.1090/S0002-9939-1991-1031450-5
- MathSciNet review: 1031450