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Displaying similar documents to “Group rings with FC-nilpotent unit groups.”

Some remarks on almost finitely generated nilpotent groups.

Peter Hilton, Robert Militello (1992)

Publicacions Matemàtiques

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We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp ≅ Hp for all p. The we have proper set-inclusions: {fg} ⊂ {fg-like} ⊂ {fgp}. We examine the extent to which fg-like nilpotent groups satisfy the axioms for...

On a theorem of Schur.

Hilton, Peter (2001)

International Journal of Mathematics and Mathematical Sciences

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On Kolchin's theorem.

Israel N. Herstein (1986)

Revista Matemática Iberoamericana

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A well-known theorem due to Kolchin states that a semi-group G of unipotent matrices over a field F can be brought to a triangular form over the field F [4, Theorem H]. Recall that a matrix A is called unipotent if its only eigenvalue is 1, or, equivalently, if the matrix I - A is nilpotent. Many years ago I noticed that this result of Kolchin is an immediate consequence of a too-little known result due to Wedderburn [6]. This result of Wedderburn asserts that if B is a finite...