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Some natural subgroups of the Nottingham group

Published online by Cambridge University Press:  20 January 2009

Rachel Camina
Rachel Camina
Affiliation:
Department of Mathematics and Computing ScienceUniversity of the South PacificSuvaFiji Islands E-mail address: [email protected]
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The Nottingham group can be described as the group of normalized automorphisms of the ring Fp[[t]], namely, those automorphisms acting trivially on tFp[[t]]/t2Fp[[t]]. In this paper we consider certain proper subgroups of the Nottingham group. We prove that these subgroups are identical to their normalizers and that some of them are isomorphic to the Nottingham group.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 333 - 339
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Camina, R., Subgroups of the Nottingham group, J. Algebra 196 (1997), 101–113.CrossRefGoogle Scholar
2.Dixon, J. D., du Sautoy, M. P. F., Mann, A. and Segal, D., Analytic pro-p Groups (London Mathematical Society Lecture Note Series 157, Cambridge University Press, Cambridge, 1991).Google Scholar
3.Klaas, G., Leedham-Green, C. R. and Plesken, W., Linear Pro-p-Groups of Finite Width (Lecture Notes in Mathematics 1674, Springer-Verlag, Berlin-Heidelberg, 1997).CrossRefGoogle Scholar
4.Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin-Heidelberg, 1967).CrossRefGoogle Scholar
5.Jennings, S. A., Substitution groups of formal power series, Canad. J. Math. 6 (1954), 325–340.CrossRefGoogle Scholar
6.Johnson, D. L., The group of formal power series under substitution, J. Austral. Math. Soc. 45 (1988), 296–302.CrossRefGoogle Scholar
7.Leedham-Green, C. R., The structure of finite p-groups, J. London Math. Soc. 50 (1994), 49–67.CrossRefGoogle Scholar
8.Shalev, A., The structure of finite p-groups: effective proof of the coclass conjectures, Invent. Math. 115 (1994), 315–345.CrossRefGoogle Scholar
9.York, I. O., The exponent of certain p-groups, Proc. Edinburgh Math. Soc. 33 (1990), 483–490.CrossRefGoogle Scholar
10.York, I. O., The group of formal power series (Ph.D Thesis, Nottingham University, 1990).Google Scholar