A note on uniserial loops

Jaroslav Ježek; Tomáš Kepka

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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.

A-loops close to code loops are groups

Aleš Drápal (2000)

Commentationes Mathematicae Universitatis Carolinae

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Let $Q$ be a diassociative A-loop which is centrally nilpotent of class 2 and which is not a group. Then the factor over the centre cannot be an elementary abelian 2-group.

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 “A note on uniserial loops”

Bol-loops of order 3 · 2 n

A-loops close to code loops are groups

On the uniqueness of loops M ( G , 2 )

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

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