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AUTOMORPHISMS OF RELATIVELY FREE GROUPS IN THE VARIETY N2A ∧ AN2 ∧ Nc

Published online by Cambridge University Press:  05 July 2001

ATHANASSIOS I. PAPISTAS
ATHANASSIOS I. PAPISTAS
Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki GR 54006, Greece; [email protected]
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Abstract

For positive integers n and c, with n [ges ] 2, let Gn, c be a relatively free group of finite rank n in the variety N2A ∧ AN2 ∧ 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.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 607 - 622
Copyright
The London Mathematical Society 2001

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