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In this paper we introduce perfectly supportable semigroups and prove that they are σ-discrete in each Hausdorff shiftinvariant topology. The class of perfectly supportable semigroups includes each semigroup S such that FSym(X) ⊂ S ⊂ FRel(X) where FRel(X) is the semigroup of finitely supported relations on an infinite set X and FSym(X) is the group of finitely supported permutations of X.

Permutation group extension of groupoids.

L. Sin-Min (1977)

Publications de l'Institut Mathématique [Elektronische Ressource]

Permutation Groups of Even Degree Whose 2-Point Stabilisers are Isomorphic Cyclic 2-Groups.

Alan R. Camina (1979)

Mathematische Zeitschrift

Permutation polynomials in several variables over finite fields

Gary Mullen (1976)

Acta Arithmetica

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...

Perspectivities in Irreducible Collineation Groups of Projective Planes. I.

Christoph Hering, Michael Walker (1977)

Mathematische Zeitschrift

Phénomène de cutoff pour certaines marches aléatoires sur le groupe symétrique

Sandrine Roussel (2000)

Colloquium Mathematicae

The main purpose of this paper is to exhibit the cutoff phenomenon, studied by Aldous and Diaconis [AD]. Let $Q^{* k}$ denote a transition kernel after k steps and π be a stationary measure. We have to find a critical value $k_{n}$ for which the total variation norm between $Q^{* k}$ and π stays very close to 1 for $k ≪ k_{n}$ , and falls rapidly to a value close to 0 for $k \geq k_{n}$ with a fall-off phase much shorter than $k_{n}$ . According to the work of Diaconis and Shahshahani [DS], one can naturally conjecture, for a conjugacy class with...

Pointwise periodic groups

K. Hofmann, F. Wright (1963)

Fundamenta Mathematicae

Polarities of G. Higman's symmetric design and a strongly regular graph on 176 vertices.

A.E. Brouwer (1982)

Aequationes mathematicae

Polynomial Automorphisms Over Finite Fields

Maubach, Stefan (2001)

Serdica Mathematical Journal

It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

Maubach, Stefan, Willems, Roel (2011)

Serdica Mathematical Journal

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.If F is a polynomial automorphism over a finite field Fq in dimension n, then it induces a permutation pqr(F) of (Fqr)n for every r О N*. We say that F can be “mimicked” by elements of a certain group of automorphisms G if there are gr О G such that pqr(gr) = pqr(F). Derksen’s theorem in characteristic zero states that the tame automorphisms in dimension n і 3 are generated by the affine maps and the one map (x1+x22, x2,ј, xn). We show...

Possible cardinalities of maximal abelian subgroups of quotients of permutation groups of the integers

Saharon Shelah, Juris Steprāns (2007)

Fundamenta Mathematicae

If G is a group then the abelian subgroup spectrum of G is defined to be the set of all κ such that there is a maximal abelian subgroup of G of size κ. The cardinal invariant A(G) is defined to be the least uncountable cardinal in the abelian subgroup spectrum of G. The value of A(G) is examined for various groups G which are quotients of certain permutation groups on the integers. An important special case, to which much of the paper is devoted, is the quotient of the full symmetric group by the...

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