Pseudoautomorphisms of Bruck loops and their generalizations

Mark Greer; Michael Kinyon

Displaying similar documents to “Pseudoautomorphisms of Bruck loops and their generalizations”

Identities and the group of isostrophisms

Aleš Drápal, Viktor Alekseevich Shcherbakov (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we reexamine the concept of isostrophy. We connect it to the notion of term equivalence, and describe the action of dihedral groups that are associated with loops by means of isostrophy. We also use it to prove and present in a new way some well known facts on $m$ -inverse loops and middle Bol loops.

Bol-loops of order $3 \cdot 2^{n}$

Daniel Wagner, Stefan Wopperer (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this article we construct proper Bol-loops of order $3 \cdot 2^{n}$ using a generalisation of the semidirect product of groups defined by Birkenmeier and Xiao. Moreover we classify the obtained loops up to isomorphism.

On the uniqueness of loops $M (G, 2)$

Petr Vojtěchovský (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let $G$ be a finite group and $C_{2}$ the cyclic group of order 2. Consider the 8 multiplicative operations $(x, y) \mapsto {(x^{i} y^{j})}^{k}$ , where $i, j, k \in {- 1, 1}$ . Define a new multiplication on $G \times C_{2}$ by assigning one of the above 8 multiplications to each quarter $(G \times {i}) \times (G \times {j})$ , for $i, j \in C_{2}$ . If the resulting quasigroup is a Bol loop, it is Moufang. When $G$ is nonabelian then exactly four assignments yield Moufang loops that are not associative; all (anti)isomorphic, known as loops $M (G, 2)$ .

Displaying similar documents to “Pseudoautomorphisms of Bruck loops and their generalizations”

Identities and the group of isostrophisms

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On the uniqueness of loops M ( G , 2 )

Bol-loops of order $3 \cdot 2^{n}$

On the uniqueness of loops $M (G, 2)$