Illinois Journal of Mathematics

Artinian-finitary groups over commutative rings

B. A. F. Wehrfritz

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Let $M$ be a module over the commutative ring $R$. We consider the group $G$ of all automorphisms $g$ of $M$ for which $M(g-1)$ is $R$-Artinian. We show that $G$ has a locally residually nilpotent normal subgroup modulo which $G$ is a subdirect product of finitary linear groups over field images of $R$. This can be used to study certain subgroups of $G$. For example, if $H$ is a locally finite subgroup of $G$, then $H$ is isomorphic to a finitary linear group of characteristic zero if $R$ is an algebra over the rationals and $H/O_p(H)$ is isomorphic to a finitary linear group of characteristic the prime $p$ if R has characteristic a power of $p$. It also gives information about $\operatorname{Aut}_RM$ if $M$ itself is $R$-Artinian.

Article information

Illinois J. Math., Volume 47, Number 1-2 (2003), 551-565.

First available in Project Euclid: 17 November 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F28: Automorphism groups of groups [See also 20E36]


Wehrfritz, B. A. F. Artinian-finitary groups over commutative rings. Illinois J. Math. 47 (2003), no. 1-2, 551--565. doi:10.1215/ijm/1258488172.

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