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Automorphisms of nilpotent-by-abelian groups

Published online by Cambridge University Press:  17 April 2009

C.K. Gupta  and
Frank Levin
C.K. Gupta
Affiliation:
Department of MathematicsUniversity of ManitobaWinnipeg R3T 2N2Canada
Frank Levin
Affiliation:
Mathęematisches InstitutRuhr Universität463 BochumWest Germany
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Abstract

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For F free of rank 4, a generating set for Aut (F/[F′, F′, F′]) exhibiting countably many wild automorphisms is obtained. Also included are examples of wild automorphisms in Aut (F/Vk+1) which are tame in Aut (F/Vk) for k ≥ 1, where Vk = [F″, F,…, F] (F repeats k times).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 2 , October 1989 , pp. 207 - 213
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Bachmuth, S., ‘Automorphisms of free metabelian groups’, Trans. Amer. Math. Soc. 118 (1965), 93–104.CrossRefGoogle Scholar
[2]Bachmuth, S. and Mochizuki, H.Y., ‘IA-Automorphisms of the free metabelian group of rank 3’, J. Algebra 55 (1978), 106–115.CrossRefGoogle Scholar
[3]Bachmuth, S. and Mochizuki, H.Y., ‘The nonfinite generation of Aut (G), G free metabeian of rank 3’, Trans. Amer. Meth. Soc. 270 (1982), 693–699.Google Scholar
[4]Bachmuth, S. and Mochizuki, H.Y., ‘Aut (F) → Aut (F/F″) is surjective for free group F of rank ≥ 4’, Trans. Amer. Math. Soc. 292 (1985), 81–101.Google Scholar
[5]Birman, J.S., ‘An inverse function theorem for free groups’, Proc. Amer. Math. Soc. 41 (1974), 634–638.CrossRefGoogle Scholar
[6]Bryant, R.M. and Gupta, C.K., ‘Characteristic subgroups of free centre-by-metabelian groups’, J. London Math. Soc.(2) 29 (1984), 435–440.CrossRefGoogle Scholar
[7]Chein, O., ‘IA-automorphisms of free and free metabelian groups’, Comm. Pure Appl. Math. 21 (1968), 605–629.CrossRefGoogle Scholar
[8]Gupta, Narain, Free Group Rings 66, Contemp. Math. (Amer. Math. Soc., 1987).CrossRefGoogle Scholar
[9]Nielsen, J., ‘Die Isomorphismengruppe der freien Gruppen’, Math. Ann. 91 (1924), 169–209.CrossRefGoogle Scholar
[10]Stöhr, E., ‘On automorphisms of free centre-by-metabelian groups’, Arch. Math. 48 (1987), 376–380.CrossRefGoogle Scholar