The lattice of equational theories. Part III: Definability and automorphisms
The local lifting problem for actions of finite groups on curves
Let be an algebraically closed field of characteristic . We study obstructions to lifting to characteristic the faithful continuous action of a finite group on . To each such a theorem of Katz and Gabber associates an action of on a smooth projective curve over . We say that the KGB obstruction of vanishes if acts on a smooth projective curve in characteristic in such a way that and have the same genus for all subgroups . We determine for which the KGB obstruction...
The Mathieu group and its pseudogroup extension .
The maximum distinguishing number of a group.
The Milgram non-operad
C. Berger claimed to have constructed an -operad-structure on the permutohedras, whose associated monad is exactly the Milgram model for the free loop spaces. In this paper I will show that this statement is not correct.
The multiplicative group of a local skew field as Galois group.
The Nonexistence of Certain Moufang Polygons.
The permutation group induced on a moiety.
The permutation group method for the dilogarithm
We give qualitative and quantitative improvements on all the best previously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying our permutation group method to the diophantine study of double integrals of rational functions related to the dilogarithm.
The prevalence of permutations with infinite cycles
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 of category,...
The Primitive Permutation Groups of Some Special Degrees.
The Primitive Permutation Groups of Some Special Degrees, II: Small Multiples of Certain Large Primes.
The Riemann theorem and divergent permutations
In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series of real terms is rearranged by p to a divergent series . All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied.
The set of ergodic groups of universal algebras
The small index property for algebras.
The small index property for quadratic spaces.
The structure of the automorphism group of a Croisot-Tessier semigroup.
The structure of the centralizer of a permutation.
The symmetric group of degree six can be covered by 13 and no fewer proper subgroups.
Théorèmes sur les groupes de substitutions