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Direct finiteness of group rings – a simple proof of the Kaplansky’s conjecture for finite groups. (English) Zbl 0711.16019

The author presents a simple proof of the following assertion: if H is any subgroup of a countable direct product of finite groups and F is any field, then the group algebra FH satisfies the property \(xy=1\Rightarrow yx=1\) for all x, \(y\in FH\).
Reviewer: G.Karpilovsky

MSC:

16S34 Group rings
16U60 Units, groups of units (associative rings and algebras)
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
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