2019
Том 71
№ 6

# Finitary groups and Krull dimension over the integers

Wehrfritz B. A. F.

Abstract

Let $M$ be any Abelian group. We make a detailed study for reasons explained in the Introduction of the normal subgroup $$F_\infty Aut M = \{ g \in Aut M: M(g - 1) is\;a \;minimax\; group\}$$ 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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 10, pp 1481-1500.

Citation Example: Wehrfritz B. A. F. Finitary groups and Krull dimension over the integers // Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1310–1325.

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