Skip to main content

Centralizers in locally finite groups

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1281))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Adian, The Burnside problem and identities in groups, trans. John Lennox and James Wiegold, Springer-Verlag, Berlin, New York, 1979.

    Book  Google Scholar 

  2. J.L. Alperin, "Automorphisms of solvable groups", Proc. Amer. Math. Soc. 13 (1962), 175–180.

    Article  MathSciNet  MATH  Google Scholar 

  3. A.O. Asar, "On a problem of Kegel and Wehrfritz", J. Algebra 59 (1979), 47–55.

    Article  MathSciNet  MATH  Google Scholar 

  4. A.O. Asar, "The solution of a problem of Kegel and Wehrfritz", Proc. London Math. Soc. (3) 45 (1982), 337–364.

    Article  MathSciNet  MATH  Google Scholar 

  5. V.V. Belyaev and N.F. Sesekin, "Periodic groups with an almost regular involutive automorphism," Studia Sci. Math. Hungar. 17 (1982), 137–141.

    MathSciNet  MATH  Google Scholar 

  6. A.V. Borovik, "Embeddings of finite Chevalley groups and periodic linear groups," Sibirsk. Mat. Zh. 24 (1983), 26–35 (Russian) = Siberian Math. J. 24 (1983), 843–55.

    MathSciNet  MATH  Google Scholar 

  7. P. Fong, "On orders of finite groups and centralizers of p-elements," Osaka J. Math. 13 (1976), 483–489.

    MathSciNet  MATH  Google Scholar 

  8. P. Hall, "A contribution to the theory of groups of prime power order," Proc. London Math. Soc. (2) 36 (1934), 29–95.

    Article  MathSciNet  MATH  Google Scholar 

  9. P. Hall and C.R. Kulatilaka, "A property of locally finite groups," J. London Math. Soc. 39 (1964), 235–239.

    Article  MathSciNet  MATH  Google Scholar 

  10. B. Hartley and Th. Meixner, "Periodic groups in which the centralizer of an involution has bounded order," J. Algebra 64 (1980), 285–291.

    Article  MathSciNet  MATH  Google Scholar 

  11. B. Hartley, Centralizers in locally finite groups, Lecture Notes No. 12, Department of Mathematics, National University of Singapore, 1982.

    Google Scholar 

  12. B. Hartley and Th. Meixner, "Finite soluble groups in which the centralizer of an element of prime order is small," Arch. Math. 36 (1981), 211–213.

    Article  MathSciNet  MATH  Google Scholar 

  13. B. Hartley, "Periodic locally soluble groups containing an element of prime order with Černikov centralizer," Quart. J. Math. Oxford (2) 33 (1982), 309–323.

    Article  MathSciNet  MATH  Google Scholar 

  14. B. Hartley and G. Shute, "Monomorphisms and direct limits of finite groups of Lie type," Quart. J. Math. Oxford (2) 35 (1984), 49–71.

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Hartley, "Fixed points of automorphisms of prime power order of locally finite groups and Chevalley groups", in preparation.

    Google Scholar 

  16. B. Hartley, Topics in the theory of nilpotent groups, in Group Theory. Essays for Philip Hall (Academic Press, London, 1984).

    Google Scholar 

  17. G. Higman, "Groups and rings having automorphisms without non-trivial fixed points," J. London Math. Soc. 32 (1957), 321–334.

    Article  MathSciNet  MATH  Google Scholar 

  18. E.I. Huhro, "Finite p-groups admitting an automorphism of order p with a small number of fixed points," Mat. Zametki 38 (1985), 652–657 (Russian).

    MathSciNet  Google Scholar 

  19. M.I. Kargapolov, "On the problem of O. Yu. Šmidt, Sibirsk. Mat. Zh. 4 (1963), 233–235.

    Google Scholar 

  20. O.H. Kegel and B.A.F. Wehrfritz, Locally finite groups (North Holland, Amsterdam, 1973).

    MATH  Google Scholar 

  21. O.H. Kegel and B.A.F. Wehrfritz, "Strong finiteness conditions in locally finite groups," Math. Z. 117 (1970), 309–324.

    Article  MathSciNet  MATH  Google Scholar 

  22. Th. Meixner, Uber endliche Gruppen mit Automorphismen, deren Fixpunktgruppe beschränkt sind (Doctoral thesis, Universität Erlangen-Nürnberg, 1979).

    Google Scholar 

  23. Th. Meixner, "Metabelsche Gruppen mit einem fixpunktfreien Automorphismus von Primzahlordnung," Arch. Math. 35 (1980), 497–500.

    Article  MathSciNet  MATH  Google Scholar 

  24. Th. Meixner, "Solvable groups admitting an automorphism of prime power order whose centralizer is small," J. Algebra 99 (1986), 181–190.

    Article  MathSciNet  MATH  Google Scholar 

  25. I.I. Pavlyuk, "On a problem of Kegel and Wehrfritz", Proc. Seventh All-Union Symposium on Group Theory, Krasnoyarsk, 1980.

    Google Scholar 

  26. A.A. Šafiro and V.P. Šunkov, "Locally finite groups with Černikov centralizers of involutions," in Studies in Group Theory, Inst. Fiz. im Kirenskogo Sibirsk. Otdel Akad. Nauk SSSR, Krasnoyarsk, 1975.

    Google Scholar 

  27. A.A. Šafiro and V.P. Šunkov, "A characterization of an infinite Černikov group which is not a finite extension of a quasicyclic group," Mat. Sb. (N.S.) 107 (149)(1978), 289–303.

    MathSciNet  Google Scholar 

  28. R. Steinberg, Endomorphisms of algebraic groups, Mem. Amer. Math. Soc. 80 (1968).

    Google Scholar 

  29. V. Stingl and V. Turau, "Locally finite Syl*p-groups," J. Algebra 90 (1984), 354–363.

    Article  MathSciNet  MATH  Google Scholar 

  30. V.P. Šunkov, "On the minimality problem for locally finite groups," Algebra i Logika 9 (1970), 220–248 (Russian) = Algebra and Logic 9 (1970), 137–151.

    MathSciNet  Google Scholar 

  31. V.P. Šunkov, "On periodic groups with an almost regular involution," Algebra i Logika 11 (1972), 470–493 (Russian) = Algebra and Logic 11 (1972), 260–272.

    MathSciNet  Google Scholar 

  32. Simon Thomas, "An identification theorem for the locally finite nontwisted Chevalley groups," Arch. Math. 40 (1983), 21–31.

    Article  MathSciNet  MATH  Google Scholar 

  33. Simon Thomas, "The classification of the simple periodic linear groups," Arch. Math. 41 (1983), 103–116.

    Article  MathSciNet  MATH  Google Scholar 

  34. V. Turau, "Zentralisatoren in lokal-endlichen Gruppen vom Chevalley-Typ," Arch. Math. 44 (1985), 297–308.

    Article  MathSciNet  MATH  Google Scholar 

  35. J.S. Wilson, "On groups satisfying Min-p," Proc. London Math. Soc. (3) 26 (1973), 226–248.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Otto H. Kegel Federico Menegazzo Giovanni Zacher

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Hartley, B. (1987). Centralizers in locally finite groups. In: Kegel, O.H., Menegazzo, F., Zacher, G. (eds) Group Theory. Lecture Notes in Mathematics, vol 1281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078689

Download citation

  • DOI: https://doi.org/10.1007/BFb0078689

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18399-0

  • Online ISBN: 978-3-540-47948-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics