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NORMAL AUTOMORPHISMS OF A FREE METABELIAN NILPOTENT GROUP

Published online by Cambridge University Press:  04 December 2009

GÉRARD ENDIMIONI
GÉRARD ENDIMIONI*
Affiliation:
C.M.I-Université De Provence, 39, rue F. Joliot-Curie, F-13453 Marseille Cedex 13, France e-mail: [email protected], [email protected]
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Abstract

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An automorphism φ of a group G is said to be normal if φ(H) = H for each normal subgroup H of G. These automorphisms form a group containing the group of inner automorphisms. When G is a non-abelian free (or free soluble) group, it is known that these groups of automorphisms coincide, but this is not always true when G is a free metabelian nilpotent group. The aim of this paper is to determine the group of normal automorphisms in this last case.

Keywords

20E3620F28
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 169 - 177
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Caranti, A. and Scoppola, C. M., Endomorphisms of two-generated metabelian groups that induce the identity modulo the derived subgroup, Arch. Math. 56 (1991), 218–227.CrossRefGoogle Scholar
2.Endimioni, G., Applications rationnelles d'un groupe nilpotent, C. R. Acad. Sci. Paris 314 (1992), 431–434.Google Scholar
3.Endimioni, G., Pointwise inner automorphisms in a free nilpotent group, Quart. J. Math. 53 (2002), 397–402.CrossRefGoogle Scholar
4.Kuz'min, J. V., Inner endomorphisms of metabelian groups (Russian), Sibirsk. Mat. Zh. 16 (1975), 736–744; Translation in Siberian Math. J. 16 (1976), 563–568.Google Scholar
5.Lubotzky, A., Normal automorphisms of free groups, J. Algebra 63 (1980), 494–498.CrossRefGoogle Scholar
6.Neumann, H., Varieties of groups (Springer-Verlag, Berlin, 1967).CrossRefGoogle Scholar
7.Robinson, D. J. S., A course in the theory of groups (Springer-Verlag, New York, 1996).CrossRefGoogle Scholar
8.Romanovskiĭ, N. S., Normal automorphisms of free solvable pro-p-groups (Russian). Algebra i Logika 36 (1997), 441–453; Translation in Algebra and Logic 36 (1997), 257–263.Google Scholar