7 papers · 1 filter
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…
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…
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.