Abstract
Groups form an important class of examples of simple theories; both abstractly and in the applications. They also sometimes appear unexpectedly out of general structural considerations in a context where a priori no group was given. Moreover, they are amenable to a more detailed model-theoretic study: due to the homogeneity imposed by the group law, a group in a simple theory often has a more friendly behaviour than a general simple structure.
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Bibliographical Remarks
Rahim Moosa. Definable group actions in simple theories. Preprint, 1998.
Anand Pillay. Definability and definable groups in simple theories. Journal of Symbolic Logic, 63: 788–796, 1998.
Frank O. Wagner. Groups in simple theories. Preprint, 1997.
Frank O. Wagner. Hyperdefinable groups in simple theories. Preprint, 1999.
André Weil. On algebraic groups of transformations. American Journal of Mathematics, 77: 302–271, 1955.
G. Schlichting. Operationen mit periodischen Stabilisatoren. Archiv der Mathematik (Basel), 34: 97–99, 1980.
Frank O. Wagner. Stable Groups (LMS LN 240). Cambridge University Press, Cambridge, UK, 1997.
Gregory Cherlin and Ehud Hrushovski. Permutation groups with few orbits on 5-tuples, and their infinite limits. Preprint, 1995.
Zoe Chatzidakis and Ehud Hrushovski. The model theory of difference fields. Transactions of the American Mathematical Society, 351 (8): 2997–3071, 1999.
Ehud Hrushovski and Anand Pillay. Groups definable in local fields and pseudo-finite fields. Israel Journal of Mathematics, 85: 203–262, 1994.
Ehud Hrushovski and Anand Pillay. Definable subgroups of algebraic groups over finite fields. Journal für die Reine und Angewandte Mathematik, 462: 69–91, 1995.
Bruno P. Poizat. Groupes Stables. Nur Al-Mantiq Wal-Ma’rifah, Villeurbanne, France, 1987.
Bruno P. Poizat. Sous-groupes définissables d’un groupe stable. Journal of Symbolic Logic, 46: 137–146, 1981.
Bruno P. Poizat. Groupes stables, avec types génériques réguliers. Journal of Symbolic Logic, 48: 339–355, 1983.
Ehud Hrushovski. Contributions to Stable Model Theory. PhD thesis, University of California at Berkeley, Berkeley, USA, 1986.
Ehud Hrushovski. Locally modular regular types. In John T. Baldwin, editor, Classification Theory: Proceedings of the US-Israel Binational Workshop on Model Theory in Mathematical Logic, Chicago, ’85, (LNM 1292), pages 132–164. Springer-Verlag, Berlin, Germany, 1987.
George M. Bergman and Hendrik W. Lenstra, Jr. Subgroups close to normal subgroups. Journal of Algebra, 127: 80–97, 1989.
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Wagner, F.O. (2000). Groups. In: Simple Theories. Mathematics and Its Applications, vol 503. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3002-0_4
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DOI: https://doi.org/10.1007/978-94-017-3002-0_4
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