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Periods of sets of lengths: a quantitative result and an associated inverse problem

Wolfgang A. Schmid (2008)

Colloquium Mathematicae

The investigation of quantitative aspects of non-unique factorizations in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group of this number field. In this paper we investigate the combinatorial problems related to the function 𝓟(H,𝓓,M)(x), counting elements whose sets of lengths have period 𝓓, for extreme choices of 𝓓. If the class group meets certain conditions, we obtain the value of an exponent in the asymptotic formula of this function...

Permutability of centre-by-finite groups

Brunetto Piochi (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let G be a group and m be an integer greater than or equal to 2 . G is said to be m -permutable if every product of m elements can be reordered at least in one way. We prove that, if G has a centre of finite index z , then G is ( 1 + [ z / 2 ] ) -permutable. More bounds are given on the least m such that G is m -permutable.

Permutations preserving Cesàro mean, densities of natural numbers and uniform distribution of sequences

M. Blümlinger, N. Obata (1991)

Annales de l'institut Fourier

We are interested in permutations preserving certain distribution properties of sequences. In particular we consider μ -uniformly distributed sequences on a compact metric space X , 0-1 sequences with densities, and Cesàro summable bounded sequences. It is shown that the maximal subgroups, respectively subsemigroups, of A u t ( N ) leaving any of the above spaces invariant coincide. A subgroup of these permutation groups, which can be determined explicitly, is the Lévy group 𝒢 . We show that 𝒢 is big in the...

Permutations which make transitive groups primitive

Pedro Lopes (2009)

Open Mathematics

In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive groups...

Currently displaying 61 – 80 of 325