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Inventiones mathematicae

, Volume 115, Issue 1, pp 315–345 | Cite as

The structure of finitep-groups: Effective proof of the coclass conjectures

  • Aner Shalev
Article

Keywords

Effective Proof 
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References

  1. 1.
    Alperin, J.L.: Automorphisms of solvable groups. Proc. Am. Math. Soc.13, 175–180 (1962)Google Scholar
  2. 2.
    Blackburn, N.: On a special class ofp-groups. Acta math.100, 49–92 (1958)Google Scholar
  3. 3.
    Dixon, J., du Sautoy, M.P.F., Mann, A., Segal, D.: Analytic Pro-p groups. (Lond. Math. Soc. Lect. Note Ser., vol. 157) Cambridge: Cambridge University Press 1991Google Scholar
  4. 4.
    Donkin, S.: Space groups and groups of prime power order. VIII. Pro-p groups of finite coclass andp-adic Lie algebras. J. Algebra111, 316–342 (1987)Google Scholar
  5. 5.
    Finken, H., Neubüser, J., Plesken, W.: Space groups and groups of prime power order. II. Classification of space groups by finite factor groups. Arch. Math35, 203–209 (1980)Google Scholar
  6. 6.
    Hall, P.: A contribution to the theory of groups of prime power order. Proc. Lond. Math. Soc., II Ser.36, 29–95 (1933)Google Scholar
  7. 7.
    Higman, G.: Groups and rings having automorphisms without non-trivial fixed elements. J. Lond. Math. Soc.32, 321–334 (1957)Google Scholar
  8. 8.
    Holt, D.F., Plesken W.: Thep-coclass of a group. J. Algebra (to appear)Google Scholar
  9. 9.
    Huppert, B., Blackburn, N.: Finite group II. Berlin Heidelberg New York: Springer 1982Google Scholar
  10. 10.
    Jacobson, N.: A note on automorphisms and derivations of Lie algebras. Proc. Am. Math. Soc.6, 281–283 (1955)Google Scholar
  11. 11.
    Jacobson, N.: Lie Algebras. New York: Wiley-Interscience 1962Google Scholar
  12. 12.
    James, R.: 2-groups of almost maximal class. J. Aust. Math. Soc.19, 343–357 (1975)Google Scholar
  13. 13.
    James, R.: 2-groups of coclass at most 3. (Preprint)Google Scholar
  14. 14.
    Lazard, M.: Sur les groupes nilpotents et les anneux de Lie. Ann. Sci Ec. Norm. Super71, 101–190 (1954)Google Scholar
  15. 15.
    Lazard, M.: Groupes analytiquesp-adiques. Publ. Math., Inst Hautes Étud. Sci.26, 389–603 (1965)Google Scholar
  16. 16.
    Leedham-Green, C.R.: Pro-p groups of finite coclass. (to appear)Google Scholar
  17. 17.
    Leedham-Green, C.R.: The structure of finitep-groups. (to appear)Google Scholar
  18. 18.
    Leedham-Green, C.R., McKay, S.: Onp-groups of maximal class I. Q. J. Math., Oxf., II. Ser.27, 297–311 (1976)Google Scholar
  19. 19.
    Leedham-Green, C.R., McKay, S.: Onp-groups of maximal class. II. Q. J. Math. Oxf. II. Ser.29, 175–186 (1978)Google Scholar
  20. 20.
    Leedham-Green, C.R., McKay, S.: Onp-groups of maximal class. III. Q. J. Math. Oxf. II. Ser.29, 175–186 (1978)Google Scholar
  21. 21.
    Leedham-Green, C.R., McKay, S., Plesken, W.: Space groups and groups of prime power order. V. A bound to the dimension of space groups with fixed coclass. Proc. Lond. Math. Soc.52, 73–94 (1986)Google Scholar
  22. 22.
    Leedham-Green, C.R., McKay, S., Plesken, W.: Space groups and groups of prime power order. VI. A bound to the dimension of a 2-adic group with fixed coclass. J. Lond. Math. Soc.34, 417–425 (1986)Google Scholar
  23. 23.
    Leedham-Green, C.R., Newman, M.F.: Space groups and groups of prime power order. I. Arch. Math.35, 193–202 (1980)Google Scholar
  24. 24.
    Lubotzky, A., Mann, A.: Powerfulp-groups. I. Finite groups. J. Algebra105, 484–505 (1987)Google Scholar
  25. 25.
    Mann, A.: Space groups and groups of prime power order. VII. Powerfulp-groups and uncoveredp-groups. Bull. Lond. Math. Soc.24, 271–276 (1992)Google Scholar
  26. 26.
    McKey, S.: On a special class ofp-groups. Q. J. Math. Oxf., II Ser.38, 489–502 (1987)Google Scholar
  27. 27.
    McKey, S.: On a special class ofp-groups. II. Q. J. Math. Oxf., II Ser.,41, 431–448 (1990)Google Scholar
  28. 28.
    Shalev, A.: Growth functions,p-adic analytic groups, and groups of finite coclass. J. Lond. Math. Soc.,46, 111–112 (1992)Google Scholar
  29. 29.
    Shalev, A.: On almost fixed point free automorphisms, J. Algebra157, 271–282 (1993)Google Scholar
  30. 30.
    Shalev, A., Zelmanov, E.I.: Pro-p groups of finite coclass. Math. Proc. Cambr. Philos. Soc.111, 417–421 (1992)Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Aner Shalev
    • 1
  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael

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