Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T19:01:56.554Z Has data issue: false hasContentIssue false
  • English
  • Français

THE RIGHT ANGLE TO LOOK AT ORTHOGONAL SETS

Published online by Cambridge University Press:  29 September 2016

FRANK O. WAGNER
FRANK O. WAGNER*
Affiliation:
UNIVERSITÉ DE LYON; CNRS UNIVERSITÉ CLAUDE BERNARD LYON 1 INSTITUT CAMILLE JORDAN UMR 5208 43 BD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEX, FRANCE E-mail: wagner@math.univ-lyon1.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in X ∪ Y has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developed. Moreover, a version of Schlichting’s Theorem for hyperdefinable families of commensurable subgroups is shown.

Keywords

03C45orthogonalitysimplicityinternality
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 4 , December 2016 , pp. 1298 - 1314
Copyright
Copyright © The Association for Symbolic Logic 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ben Yaacov, I., Simplicity in compact abstract theories . Journal of Mathematical Logic, vol. 3 (2003), no. 2, pp. 163–191.CrossRefGoogle Scholar
Berarducci, A. and Mamino, M., Groups definable in two orthogonal sorts . Israel Journal of Mathematics, vol. 208 (2015), no. 1, pp. 413–441.Google Scholar
Bergman, G. M. and Lenstra, H. W. Jr., Subgroups close to normal subgroups . Journal of Algebra, vol. 127 (1989), pp. 80–97.CrossRefGoogle Scholar
Blossier, T., Martín Pizarro, A. and Wagner, F. O., A la recherche du tore perdu , this Journal, vol. 81 (2016), no. 1, pp. 1–31.Google Scholar
Casanovas, E., Simple Theories and Hyperimaginaries, Lecture Notes in Logic 39, Cambridge University Press, Cambridge, UK, 2011.Google Scholar
Schlichting, G., Operatoren mit periodischen Stabilisatoren . Archives of Mathematics ( Basel ), vol. 34 (1980), pp. 97–99.Google Scholar
Wagner, F. O., Simple Theories, Mathematics and its Applications 503, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.CrossRefGoogle Scholar