KT-nearfields of rank 2.
k-transitive Permutation Groups and k-planes.
Landau’s function for one million billions
Let denote the symmetric group with letters, and the maximal order of an element of . If the standard factorization of into primes is , we define to be ; one century ago, E. Landau proved that and that, when goes to infinity, .There exists a basic algorithm to compute for ; its running time is and the needed memory is ; it allows computing up to, say, one million. We describe an algorithm to calculate for up to . The main idea is to use the so-called -superchampion...
Large free subgroups of automorphism groups of ultrahomogeneous spaces
We consider the following notion of largeness for subgroups of . A group G is large if it contains a free subgroup on generators. We give a necessary condition for a countable structure A to have a large group Aut(A) of automorphisms. It turns out that any countable free subgroup of can be extended to a large free subgroup of , and, under Martin’s Axiom, any free subgroup of of cardinality less than can also be extended to a large free subgroup of . Finally, if Gₙ are countable groups, then...
Le diagramme du treillis permutoèdre est intersection des diagrammes de deux produits directs d'ordres totaux
Deux codages sont utilisés sur l’ensemble des permutations ou ordres totaux sur un ensemble fini à éléments et à chacun de ces codages est associé un produit direct d’ordres totaux. On démontre que le diagramme du treillis permutoèdre (ou ordre de Bruhat faible sur le groupe symétrique ) est intersection des diagrammes des deux produits directs de ordres totaux à éléments.
Linear dependence of zeros of polynomials and construction of primitve elements.
Linear groups with large cyclic subgroups and translation planes
Line-transitive automorphism groups of linear spaces.
Locally finite classical Tits chamber Systems of large order.
Majoration explicite de l'ordre maximum d'un élément du groupe symétrique
Malnormal subgroups and Frobenius groups: basics and examples
Malnormal subgroups occur in various contexts. We review a large number of examples, and compare the general situation to that of finite Frobenius groups of permutations.In a companion paper [18], we analyse when peripheral subgroups of knot groups and -manifold groups are malnormal.
Matroid automorphisms of the root system.
Maximal clones and maximal permutation groups
A fundamental result in universal algebra is the theorem of Rosenberg describing the maximal subclones in the clone of all operations over a finite set. In group theory, the maximal subgroups of the symmetric groups are classified by the O'Nan-Scott Theorem. We shall explore the similarities and differences between these two analogous major results. In addition, we show that a primitive permutation group of diagonal type can be maximal in the symmetric group only if its socle is the direct product...
Maximal ...-Subgroups of the Symmetric Groups.
McKay numbers and heights of characters.
Mémoire sur la résolution des équations algébriques les unes par les autres.
Modular permutations on
Monochrome symmetric subsets in 2-colorings of groups.
Multiples of left loops and vertex-transitive graphs
Via representation of vertex-transitive graphs on groupoids, we show that left loops with units are factors of groups, i.e., left loops are transversals of left cosets on which it is possible to define a binary operation which allows left cancellation.
Multiplication groups of free loops. I