Finitary groups and Krull dimension over the integers

  • B. A. F. Wehrfritz

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.
Published
25.10.2006
How to Cite
Wehrfritz, B. A. F. “Finitary Groups and Krull Dimension over the Integers”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 10, Oct. 2006, pp. 1310–1325, https://umj.imath.kiev.ua/index.php/umj/article/view/3534.
Section
Research articles