Displaying similar documents to “The construction of affine structures on virtually nilpotent groups.”

On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus

Rafał Pikuła (2010)

Studia Mathematica

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Let G be a group generated by a set of affine unipotent transformations T: X → X of the form T(x) = A x + α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. We show that the enveloping semigroup E(X,G) of the dynamical system (X,G) is a nilpotent group and find upper and lower bounds on its nilpotency class. Also, we obtain a description of E(X,G) as a quotient space.

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...

Nil series from arbitrary functions in group theory

Ian Hawthorn (2018)

Commentationes Mathematicae Universitatis Carolinae

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In an earlier paper distributors were defined as a measure of how close an arbitrary function between groups is to being a homomorphism. Distributors generalize commutators, hence we can use them to try to generalize anything defined in terms of commutators. In this paper we use this to define a generalization of nilpotent groups and explore its basic properties.