10 papers
Construction of groups with triality and their corresponding code loops
Rosemary Miguel Pires, Alexandre Grishkov, Rodrigo Lucas Rodrigues +1
We generalize the global construction of code loops introduced by Nagy, which is based on the connection between Moufang loops and groups with triality. This follows from the const…
The half-automorphism group of code loops
Dylene Agda Souza de Barros, Alexandre Grishkov, Rosemary Miguel Pires +1
For any code loop , we prove that the half-automorphism group of is the product of the automorphism group of by an elementary abelian group consisting of all half-au…
Representations of code loops by binary codes
Rosemary Miguel Pires, Alexandre Grishkov, Marina Rasskazova
Code loops are Moufang loops constructed from doubly even binary codes. Then, given a code loop , we ask which doubly even binary code produces . In this sense, is ca…
Free Bol loops of exponent two
Alexandre Grishkov, Marina Rasskazova, Giliard Souza dos Anjos
A Bol loop is a loop that satisfies the identity . In this paper, we give a construction of the free Bol loops of exponent two. We define a canonical form of all…
On Malcev algebras nilpotent by Lie center and corresponding analytic Moufang loops
Alexander Grishkov, Marina Rasskazova, Liudmila Sabinina +1
In this note we describe the structure of finite dimensional Malcev algebras over a field of real numbers , which are nilpotent module its Lie center. It is proved that…
Representations of code loops by binary codes
Rosemary Miguel Pires, Alexandre Grishkov, Marina Rasskazova
Code loops are Moufang loops constructed from doubly even binary codes. Then, given a code loop L, we ask which doubly even binary code V produces L. In this sense, V is called a r…
Automorphic loops arising from module endomorphisms
Alexandr Grishkov, Marina Rasskazova, Petr Vojtěchovský
A loop is automorphic if all its inner mappings are automorphisms. We construct a large family of automorphic loops as follows. Let be a commutative ring, an -module, $E…
Moufang Theorem for a variety of local non-Moufang loops
Ramiro Carrillo-Catalán, Liudmila Sabinina, Marina Rasskazova
An open problem in theory of loops is to find the variety of non- Moufang loops satisfying the Moufang Theorem. In this note, we present a variety of local smooth diassociative loo…
Malcev algebras corresponding to smooth Almost Left Automorphic Moufang Loops
Ramiro Carrillo-Catalán, Marina Rasskazova, Liudmila Sabinina
In this note we introduce the concept of an almost left automorphic Moufang loop and study the properties of tangent algebras of smooth loops of this class.
Nilpotent Steiner loops of class 2
A. Grishkov, D. Rasskazova, M. Rasskazova +1
We describe Steiner loops of nilpotency class 2 and establish the classification of finite 3-generated nilpotent Steiner loops of nilpotency class 2.