Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T07:46:55.711Z Has data issue: false hasContentIssue false
  • English
  • Français

Pro-p groups of finite coclass

Published online by Cambridge University Press:  24 October 2008

A. Shalev  and
E. I. Zelmanov
A. Shalev
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford OX1 3LB
E. I. Zelmanov
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford OX1 3LB
Get access Rights & Permissions [Opens in a new window]

Extract

In 1980 Leedham-Green and Newman made a series of conjectures on the structure of pro-p groups and finite p-groups of a given coclass [10]. These insightful conjectures have gradually been proved, in a series of papers (some of which are still unpublished) by Leedham-Green, Donkin, McKay and Plesken (see, e.g. [11, 2, 8, 9, 13, 14]). Some simplifications (as well as additional information) have recently been given in [12, 15].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 3 , May 1992 , pp. 417 - 421
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Alperin, J. L.. Automorphisms of solvable groups. Proc. Amer. Math. Soc. 13 (1962), 175–180.CrossRefGoogle Scholar
[2]Donkin, S.. Space groups and groups of prime power order. VIII. Pro-p groups of finite coclass and p-adic Lie algebras. J. Algebra 111 (1987), 316–342.CrossRefGoogle Scholar
[3]Dixon, J., du Sautoy, M. P. F., Mann, A. and Segal, D.. Analytic pro-p Groups. London Math. Soc. Lecture Note Ser. no. 157 (Cambridge University Press, 1991).Google Scholar
[4]Huppert, B. and Blackburn, N.. Finite Groups, vol. 2 (Springer-Verlag, 1982).Google Scholar
[5]Jacobson, N.. Lie Algebras (Wiley-Interscience, 1962).Google Scholar
[6]Kreknin, V. A.. Solvability of Lie algebras with a regular automorphism of finite period. Soviet Mat. Dokl. 4 (1963), 683–685.Google Scholar
[7]Lazard, M.. Groupes analytiques p-adiques. Inst. Hautes Études Sci. Publ. Math. 26 (1965), 389–603.Google Scholar
[8]Leedham-Green, C. R.. pro-p groups of finite coclass. Preprint.Google Scholar
[9]Leedham-Green, C. R.. The structure of finite p-groups. Preprint.Google Scholar
[10]Leedham-Green, C. R. and Newman, M. F.. Space groups and groups of prime power order I. Arch. Math. (Basel) 35 (1980), 193–202.CrossRefGoogle Scholar
[11]Leedham-Green, C. R., McKay, S. and Plesken, W.. Space groups and groups of prime power order. V. A bound to the dimension of space groups with fixed coclass. Proc. London Math. Soc. (3) 52 (1986), 73–94.CrossRefGoogle Scholar
[12]Mann, A.. Space groups and groups of prime power order. VII. Powerful p-groups and uncovered p-groups. Bull. London Math. Soc., to appear.Google Scholar
[13]McKay, S.. On the structure of a special class of p-groups. Quart. J. Math. Oxford Ser. (2), 38 (1987), 489–502.CrossRefGoogle Scholar
[14]McKay, S.. On the structure of a special class of p-groups II. Quart. J. Math. Oxford Ser. (2), 41 (1990), 431–448.CrossRefGoogle Scholar
[15]Shalev, A.. Growth functions, p-adic analytic groups, and groups of finite coclass. J. London Math. Soc., to appear.Google Scholar
[16]Shalev, A.. On almost fixed point free automorphisms. J. Algebra, to appear.Google Scholar