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We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group $Sym (ℕ)$ as its additive group.

Opérades cellulaires et espaces de lacets itérés

Clemens Berger (1996)

Annales de l'institut Fourier

L’espace des configurations de $p$ points distincts de $R^{\infty}$ admet une filtration naturelle qui est induite par les inclusions des $R^{n}$ dans $R^{\infty}$ . Nous caractérisons le type d’homotopie de cette filtration par les propriétés combinatoires d’une structure cellulaire sous-jacente, étroitement liée à la théorie des $E_{n}$ -opérades de May. Cela donne une approche unifiée des différents modèles combinatoires d’espaces de lacets itérés et redémontre les théorèmes d’approximation de Milgram, Smith et Kashiwabara.

Partition identities with an application to group representation theory.

Jorn B. Olsson, George E. Andrews (1991)

Journal für die reine und angewandte Mathematik

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...

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...

Presentation of the singular part of the Brauer monoid

Victor Maltcev, Volodymyr Mazorchuk (2007)

Mathematica Bohemica

We obtain a presentation for the singular part of the Brauer monoid with respect to an irreducible system of generators consisting of idempotents. As an application of this result we get a new construction of the symmetric group via connected sequences of subsets. Another application describes the lengths of elements in the singular part of the Brauer monoid with respect to the system of generators mentioned above.

Pseudo-galois Extensions of Boolean Algebras

Žikica Perović (1993)

Publications de l'Institut Mathématique

Quelques propriétés d'une certaine classe d'opérateurs définis sur les groupes symétriques (fixateurs et biinvodécompositions)

Max Fontet, André Lentin (1969/1970)

Séminaire Schützenberger

Recognition by the set of element orders of symmetric groups of degree $r$ and $r + 1$ for prime $r$ .

Zavarnitsin, A.V. (2002)

Sibirskij Matematicheskij Zhurnal

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)

Commentationes Mathematicae Universitatis Carolinae

This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra $𝔽 S_{n}$ of the symmetric group $S_{n}$ over a field $𝔽$ of characteristic 0 (or $p > n$ ). The goal is to obtain a constructive version of the isomorphism $ψ : ⨁_{λ} M_{d_{λ}} (𝔽) ⟶ 𝔽 S_{n}$ where $λ$ is a partition of $n$ and $d_{λ}$ counts the standard tableaux of shape $λ$ ....

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Maximal ...-Subgroups of the Symmetric Groups.

Note sur les bases du groupe symétrique.

On a constant of Turán and Erdös

On $q$ -analogs of recursions for the number of involutions and prime order elements in symmetric groups.

On the maximal order in $S_{n}$ and $S *_{n}$

On the number of permutations arising from a problem in cell-biology.

On the number of rim hook tableaux

On zero-symmetric nearrings with identity whose additive groups are simple