Skip to main content
Log in

Una nota sui gruppi policiclici che ammettono un automorfismo con numero di Reidemeister finito

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

LetG be a group and ϕ an automorphism ofG. Two elementsx, y ∈ G are called ϕ-conjugate if there existsg ∈ G such thatx=g −1 yg θ. It is easily verified that the ϕ-conjugation is an equivalence relation; the numberR(ϕ) of ϕ-classes ofG is called the Reidemeister number of the automorphism ϕ.

In this paper we prove that if a polycyclic groupsG admits an automorphism ϕ of ordern such thatR(ϕ)<∞, thenG contains a subgroup of finite index with derived length at most 2n−1.

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

  1. A. Fel’shtyn — R. Hill.The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion, K-Theory,8 (1994), 367–393.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Gonçalves — P. Wong.Twisted conjugacy classes in exponential growth groups, Bull. London Math. Soc.,35 (2003), 261–268.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. I. Khukhro.Nilpotent groups and their automorphisms, de Gruyter, Berlin-New York, 1993.

    MATH  Google Scholar 

  4. E. I. Khukhro.p-automorphisms of finite p-groups, Cambridge University Press, Cambridge, 1998.

    MATH  Google Scholar 

  5. A. L. Mal’cev.On certain classes of infinite solvable groups, Mat. Sb. N.S.,28 (1951) 567–588 (Russian); English transl., Amer. Math. Soc. Trans.,2 (1956), 1–21.

    MathSciNet  Google Scholar 

  6. D. J. S. Robinson.A Course in the Theory of Groups, Springer-Verlag Berlin-Heidelberg-New York, 1982.

    MATH  Google Scholar 

  7. G. Zappa.Sugli automorfismi uniformi nei gruppi di Hirsch, Ricerche Mat.,7 (1958), 3–13.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jabara, E. Una nota sui gruppi policiclici che ammettono un automorfismo con numero di Reidemeister finito. Rend. Circ. Mat. Palermo 56, 343–348 (2007). https://doi.org/10.1007/BF03032087

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03032087

MSC 2000

Navigation