相关论文: Generators for finite simple Moufang loops

We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…

This article is devoted to the investigation of semidirect products of groups of loops and groups of diffeomorphisms of finite and infinte dimensional real, complex and quaternion manifolds. Necessary statements about quaternion manifolds…

We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…

Let $F$ be a field with at least three elements and $G$ a locally finite group. This paper aims to show that if either $F$ is algebraically closed or the characteristic of $F$ is positive, then an element in the group algebra $FG$ is a…

A finite group $G$ is \emph{coprimely-invariably generated} if there exists a set of generators $\{g_1, ..., g_u\}$ of $G$ with the property that the orders $|g_1|, ..., |g_u|$ are pairwise coprime and that for all $x_1, ..., x_u \in G$ the…

Let $G$ be a finite abelian group $G$ with $N$ elements. In this paper we give a O(N) time algorithm for computing a basis of $G$. Furthermore, we obtain an algorithm for computing a basis from a generating system of $G$ with $M$ elements…

C-loops are loops satisfying $x(y(yz))=((xy)y)z$. They often behave analogously to Moufang loops and they are closely related to Steiner triple systems and combinatorics. We initiate the study of C-loops by proving: (i) Steiner loops are…

It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To…

We describe the collection of finite simple groups, with a view on physical applications. We recall first the prime cyclic groups $Z_p$, and the alternating groups $Alt_{n>4}$. After a quick revision of finite fields $\mathbb{F}_q$, $q =…

We show that the minimal number of generators and the Cohen-Macaulay type of a family of numerical semigroups generated by concatenation of arithmetic sequences is unbounded.

We classify the factorizations of finite classical groups with nonsolvable factors, completing the classification of factorizations of finite almost simple groups.

Every finite simple group can be generated by two elements and, in fact, every nontrivial element is contained in a generating pair. Groups with this property are said to be $\frac{3}{2}$-generated, and the finite $\frac{3}{2}$-generated…

We present a method to explicitly compute a complete set of orthogonal primitive idempotents in a simple component with Schur index 1 of a rational group algebra $\mathbb{Q}G$ for $G$ a finite generalized strongly monomial group. For the…

We determine the minimal number of generators of the homological Goldman Lie algebra of a surface consisting of elements of the first homology group of the surface.

Associated to any closed subgroup $G\subset U_N^+$ is a family of toral subgroups $T_Q\subset G$, indexed by the unitary matrices $Q\in U_N$. The family $\{T_Q|Q\in U_N\}$ is expected to encode the main properties of $G$, and there are…

Rational loops played a central role in Uhlenbeck's construction of harmonic maps into U(n) (chiral model in physics), and they are generated by simple elements with one pole and one zero constructed from Hermitian projections. It has been…

It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras and can be seen as a preliminary step to…

A group in which every element commutes with its endomorphic images is called an $E$-group. Our main result is that all 3-generator $E$-groups are abelian. It follows that the minimal number of generators of a finitely generated non-abelian…

The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups $B_u(Q)$ for…

We study groups generated by three half-turns in the Lobachevsky $3$-space and their quotient orbifolds. These generalized triangle groups are closely related to the arbitrary 2-generator Kleinian groups. Our main result is a classification…