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Sous-groupes periodiques d'un groupe stable

Published online by Cambridge University Press:  12 March 2014

Bruno Poizat  and
Frank Wagner
Bruno Poizat
Affiliation:
Mathématiques-Bâtiment 101, Université Claude Bernard (Lyon-I), F-69622-Villeurbanne-Cedex-, France, E-mail: poizat@lan1.univ-lyon1.fr
Frank Wagner
Affiliation:
Mathematisches Institut, Universitat Freiburg, Albertstrasse 23B 7800 Freiburg, Germany, E-mail: frwagner@ibm.ruf.uni-freiburg.de
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Abstract

We develop a Sylow theory for stable groups satisfying certain additional conditions (2- finiteness, solvability or smallness) and show that their maximal p-subgroups are locally finite and conjugate. Furthermore, we generalize a theorem of Baer-Suzuki on subgroups generated by a conjugacy class of p-elements.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 2 , June 1993 , pp. 385 - 400
Copyright
Copyright © Association for Symbolic Logic 1993

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References

REFERENCES

Baudish, Andreas [1989], On superstable groups, Seminarbericht n° 104, Humboldt Universitat zu Berlin, pp. 18–42.Google Scholar
Borovik, Aleksandr Vasilievich [1990], La théorie de Sylow des groupes de rang de Morley fini, Siberian Mathematical Journal, vol. 30, no. 6, pp. 52–57.(en russe)CrossRefGoogle Scholar
Borovik, Aleksandr Vasilievich and Poizat, Bruno Petrovich [1990], Tores et p-groupes, this Journal, vol. 55, pp.478–491.Google Scholar
Brown, K. S. [1982], Cohomology of groups, Springer-Verlag, New York.CrossRefGoogle Scholar
Bryant, Roger M. [1979], Groups with minimal condition on centralizers, Journal of Algebra, vol. 60, p. 371–383.CrossRefGoogle Scholar
Gorenstein, Daniel [1968], Finite groups, Harper and Row, New York.Google Scholar
Kegel, Otto [1989], Four lectures on Sylow theory locally finite groups, Group theory (Cheng, Nah and Leong, Yu Kaiang, editors), Walter de Gruyter, Berlin.Google Scholar
Poizat, Bruno [1987], Groupes stables, Nur al-Mantiq wal-Ma'rifah, Villeurbanne.Google Scholar
Wagner, Frank [1990], Stable groups and generic types, D. Phil. thesis, Oxford University.Google Scholar
Wagner, Frank [1990a], Subgroups of stable groups, this Journal, vol. 55, pp. 151–156.Google Scholar
Wagner, Frank [1991], Small stable groups, this Journal, vol. 56, pp. 1026–1037.Google Scholar
Wehrfritz, B. A. F. [1973], Infinite linear groups, Springer-Verlag, Berlin.CrossRefGoogle Scholar