Displaying similar documents to “A class of quasigroups solving a problem of ergodic theory”

Evaluation of divisor functions of matrices

Gautami Bhowmik (1996)

Acta Arithmetica

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1. Introduction. The study of divisor functions of matrices arose legitimately in the context of arithmetic of matrices, and the question of the number of (possibly weighted) inequivalent factorizations of an integer matrix was asked. However, till now only partial answers were available. Nanda [6] evaluated the case of prime matrices and Narang [7] gave an evaluation for 2×2 matrices. We obtained a recursion in the size of the matrices and the weights of the divisors [1,2] which helped...

Gaussian automorphisms whose ergodic self-joinings are Gaussian

Mariusz Lemańczyk, F. Parreau, J. Thouvenot (2000)

Fundamenta Mathematicae

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 We study ergodic properties of the class of Gaussian automorphisms whose ergodic self-joinings remain Gaussian. For such automorphisms we describe the structure of their factors and of their centralizer. We show that Gaussian automorphisms with simple spectrum belong to this class.  We prove a new sufficient condition for non-disjointness of automorphisms giving rise to a better understanding of Furstenberg's problem relating disjointness to the lack of common factors....

Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology

Michael Slack (1999)

Fundamenta Mathematicae

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A family of multiplicative operations in the BP Steenrod algebra is defined which is related to the total Steenrod power operation from the mod p Steenrod algebra. The main result of the paper links the BP versions of the total Steenrod power with the formal group approach to multiplicative BP operations by identifying the p-typical curves (power series) which correspond to these operations. Some relations are derived from this identification, and a short proof of the Hopf invariant...

The prevalence of permutations with infinite cycles

Randall Dougherty, Jan Mycielski (1994)

Fundamenta Mathematicae

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A number of recent papers have been devoted to the study of prevalence, a generalization of the property of being of full Haar measure to topological groups which need not have a Haar measure, and the dual concept of shyness. These concepts give a notion of "largeness" which often differs from the category analogue, comeagerness, and may be closer to the intuitive notion of "almost everywhere." In this paper, we consider the group of permutations of natural numbers. Here, in the sense...

Hyperconvexity of ℝ-trees

W. Kirk (1998)

Fundamenta Mathematicae

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It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.