The free commutative automorphic $2$-generated loop of nilpotency class $3$

Dylene Agda Souza de Barros; Alexander Grishkov; Petr Vojtěchovský

Displaying similar documents to “The free commutative automorphic $2$ -generated loop of nilpotency class $3$ ”

Commutators and associators in Catalan loops

Jan M. Raasch (2010)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Various commutators and associators may be defined in one-sided loops. In this paper, we approximate and compare these objects in the left and right loop reducts of a Catalan loop. To within a certain order of approximation, they turn out to be quite symmetrical. Using the general analysis of commutators and associators, we investigate the structure of a specific Catalan loop which is non-commutative, but associative, that appears in the original number-theoretic application of Catalan...

Pseudoautomorphisms of Bruck loops and their generalizations

Mark Greer, Michael Kinyon (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show that in a weak commutative inverse property loop, such as a Bruck loop, if $α$ is a right [left] pseudoautomorphism with companion $c$ , then $c$ [ $c^{2}$ ] must lie in the left nucleus. In particular, for any such loop with trivial left nucleus, every right pseudoautomorphism is an automorphism and if the squaring map is a permutation, then every left pseudoautomorphism is an automorphism as well. We also show that every pseudoautomorphism of a commutative inverse property loop is an automorphism,...

On multiplication groups of left conjugacy closed loops

Aleš Drápal (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A loop $Q$ is said to be left conjugacy closed (LCC) if the set ${L_{x}; x \in Q}$ is closed under conjugation. Let $Q$ be such a loop, let $ℒ$ and $ℛ$ be the left and right multiplication groups of $Q$ , respectively, and let $Inn Q$ be its inner mapping group. Then there exists a homomorphism $ℒ \to Inn Q$ determined by $L_{x} \mapsto R_{x}^{- 1} L_{x}$ , and the orbits of $[ℒ, ℛ]$ coincide with the cosets of $A (Q)$ , the associator subloop of $Q$ . All LCC loops of prime order are abelian groups.

Subloops of sedenions

Benard M. Kivunge, Jonathan D. H Smith (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

This note investigates sedenion multiplication from the standpoint of loop theory. New two-sided loops are obtained within the version of the sedenions introduced by the second author. Conditions are given for the satisfaction of standard loop-theoretical identities within these loops.

Displaying similar documents to “The free commutative automorphic 2 -generated loop of nilpotency class 3 ”

Commutators and associators in Catalan loops

Pseudoautomorphisms of Bruck loops and their generalizations

On multiplication groups of left conjugacy closed loops

Subloops of sedenions

Displaying similar documents to “The free commutative automorphic $2$ -generated loop of nilpotency class $3$ ”