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Journal of the London Mathematical Society 2001 63(3):607-622; doi:10.1017/S0024610701002058
© 2001 by London Mathematical Society
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© The London Mathematical Society

Automorphisms of Relatively Free Groups in the Variety N2A {wedge} AN2 {wedge} Nc

Athanassios I. Papistas

Department of Mathematics, Aristotle University of Thessaloniki Thessaloniki GR 54006, Greece, apapist{at}ccf.auth.gr

Received 5 October 1999. Revision received 7 July 2000.

For positive integers n and c, with n ≥ 2, let Gn, c be a relatively free group of finite rank n in the variety N2A {wedge} AN2 {wedge} Nc. It is shown that the subgroup of the automorphism group Aut(Gn, c) of Gn, c generated by the tame automorphisms and an explicitly described finite set of IA-automorphisms of Gn, c has finite index in Aut(Gn, c). Furthermore, it is proved that there are no non-trivial elements of Gn, c fixed by every tame automorphism of Gn, c.


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