On loops that are abelian groups over the nucleus and Buchsteiner loops

Piroska Csörgö

Displaying similar documents to “On loops that are abelian groups over the nucleus and Buchsteiner loops”

On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^{4}$

Markku Niemenmaa (2010)

Commentationes Mathematicae Universitatis Carolinae

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We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^{4}$ are centrally nilpotent of class at most two.

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 multiplication groups of left conjugacy closed loops

Aleš Drápal (2004)

Commentationes Mathematicae Universitatis Carolinae

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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.

A class of Bol loops with a subgroup of index two

Petr Vojtěchovský (2004)

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 $i, j \in C_{2}$ . We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P. Vojtěchovsk’y: On the uniqueness of loops $M (G, 2)$ .

Displaying similar documents to “On loops that are abelian groups over the nucleus and Buchsteiner loops”

On finite commutative IP-loops with elementary abelian inner mapping groups of order p 4

A-loops close to code loops are groups

On multiplication groups of left conjugacy closed loops

A class of Bol loops with a subgroup of index two

On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^{4}$