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Finitary groups and Krull dimension over the integers

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Abstract

Let M be any Abelian group. We make a detailed study for reasons explained in the Introduction of the normal subgroup

$$F_\infty AutM = \{ g \in AutM:M(g - 1) is a minimax group\} $$

of the automorphism group Aut M of M. The conclusions, although slightly weaker than one would hope, in that they do not fully explain the common behavior of the finitary and the Artinian-finitary subgroups of Aut M, are certainly stronger than one might reasonably expect. Our main focus is on residual properties and unipotence.

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Authors and Affiliations

  1. School of Mathemetical Sciences, Queen Mary, University of London, London, England

    B. A. F. Wehrfritz

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  1. B. A. F. Wehrfritz
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Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1310–1325, October, 2006.

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Wehrfritz, B.A.F. Finitary groups and Krull dimension over the integers. Ukr Math J 58, 1481–1500 (2006). https://doi.org/10.1007/s11253-006-0148-8

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  • DOI: https://doi.org/10.1007/s11253-006-0148-8

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