Skip to main content
Log in

Commutator conditions and splitting automorphisms for stable groups

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Summary

We show that a stable groupG satisfying certain commutator conditions is nilpotent. Furthermore, a soluble stable group with generically splitting automorphism of prime order is nilpotent-by-finite. In particular, a soluble stable group with a generic element of prime order is nilpotent-by-finite.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [BP] Boffa, M., Point, F.: Identités de Engel généralisées. Paris: C.R. Acad. Sci.313, I, 909–911 (1991)

    Google Scholar 

  • [Br] Bryant, R.M.: Groups with the Minimal Condition on Centralizers. J. Algebra60, 371–383 (1979)

    Google Scholar 

  • [Kh] Khukhro, E.I.: Nilpotency of Solvable Groups Admitting a Splitting Automorphism of Prime Order. Algebra Logika19, 118–129 (1980)

    Google Scholar 

  • [Ko] Kostrikin, A.I.: On Burnside's Problem. Izv. Akad. Nauk SSSR. Ser. Math.23, 3–34 (1959)

    Google Scholar 

  • [P1] Poizat, B.: Groupes stables. Nur al-Mantiq wal-Ma'rifah. Villeurbanne 1987

  • [P2] Poizat, B.: Equations génériques. Dahn, B., Wolter, H. (eds.) Proceedings of the 8th Easter Conference on Model Theory. Berlin: Humboldt-Universität 1990

    Google Scholar 

  • [PW] Poizat, B.P., Wagner, F.O.: Sous-groupes périodiques d'un groupe stable. J. Symb. Logic (to appear)

  • [W1] Wagner, F.O.: A propos d'équations génériques. J. Symb. Logic57, 548–554 (1992)

    Google Scholar 

  • [W2] Wagner, F.O.: Stabile Gruppen. Vorlesungsskript WS 91/92. Freiburg: Albert-Ludwigs-Universität 1992

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The author would like to thank Ali Nesin for pointing out an error in an earlier version of this paper and various valuable comments

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wagner, F.O. Commutator conditions and splitting automorphisms for stable groups. Arch Math Logic 32, 223–228 (1993). https://doi.org/10.1007/BF01375553

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01375553

Keywords

Navigation