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Displaying 1 – 16 of 16

Medial division groupoids

Tomáš Kepka (1979)

Acta Universitatis Carolinae. Mathematica et Physica

Medial quasigroups of prime square order

David Stanovský (2016)

Commentationes Mathematicae Universitatis Carolinae

We prove that, for any prime $p$ , there are precisely $2 p^{4} - p^{3} - p^{2} - 3 p - 1$ medial quasigroups of order $p^{2}$ , up to isomorphism.

Medial quasigroups of type $(n, k)$

Alena Vanžurová (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Our aim is to demonstrate how the apparatus of groupoid terms (on two variables) might be employed for studying properties of parallelism in the so called $(n, k)$ -quasigroups. We show that an incidence structure associated with a medial quasigroup of type $(n, k)$ , $n > k \geq 3$ , is either an affine space of dimension at least three, or a desarguesian plane. Conversely, if we start either with an affine space of order $k > 2$ and dimension $m$ , or with a desarguesian affine plane of order $k > 2$ then there is a medial quasigroup of...

Minimally nonassociative Moufang loops with a unique nonidentity commutator are ring alternative

Orin Chein, Edgar G. Goodaire (2002)

Commentationes Mathematicae Universitatis Carolinae

We investigate finite Moufang loops with a unique nonidentity commutator which are not associative, but all of whose proper subloops are associative. Curiously, perhaps, such loops turn out to be ``ring alternative'', in the sense that their loop rings are alternative rings.

Moufang loops arising from Zorn vector matrix algebras

Andrew Wells (2010)

Commentationes Mathematicae Universitatis Carolinae

In “A class of simple Moufang loops”, Proc. Amer. Math. Soc. 7 (1956), 471–482, Paige used the vector matrix construction over fields to produce simple Moufang loops. The purpose of this paper is to generalize the construction to the class of commutative rings, and examine the Moufang loops arising in this fashion. Specific attention is paid to the construction over the ring of integers modulo four.

Moufang loops of odd order $p_{1} p_{2} \dots p_{n} q^{3}$ .

Rajah, Andrew, Chee, Wing Loon (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Moufang loops of odd order $p_{1} p_{2} \dots p_{n} q^{3}$ with non-trivial nucleus

Andrew Rajah, Kam-Yoon Chong (2008)

Commentationes Mathematicae Universitatis Carolinae

It has been proven by F. Leong and the first author (J. Algebra 190 (1997), 474–486) that all Moufang loops of order $p^{α} q_{1}^{β_{1}} q_{2}^{β_{2}} \cdot \cdot \cdot q_{n}^{β_{n}}$ where $p$ and $q_{i}$ are odd primes, are associative if $p < q_{1} < q_{2} < \cdot \cdot \cdot < q_{n}$ , and (i) $α \leq 3$ \alpha \le 3 ...

Moufang loops of order 243

Michael C. Slattery, Ashley L. Zenisek (2012)

Commentationes Mathematicae Universitatis Carolinae

We present a computer-assisted determination of the 72 non-isomorphic, non-associative Moufang loops of order 243. Some of their properties and distinguishing features are discussed.

Moufang loops of order coprime to three that cyclically extend groups of dihedral type

Aleš Drápal (2016)

Commentationes Mathematicae Universitatis Carolinae

This paper completely solves the isomorphism problem for Moufang loops $Q = G C$ where $G ⊴ Q$ is a noncommutative group with cyclic subgroup of index two and $| Z (G) | \leq 2$ , $C$ is cyclic, $G \cap C = 1$ , and $Q$ is finite of order coprime to three.

Moufang semidirect products of loops with groups and inverse property extensions

Mark Greer, Lee Raney (2014)

Commentationes Mathematicae Universitatis Carolinae

We investigate loops which can be written as the semidirect product of a loop and a group, and we provide a necessary and sufficient condition for such a loop to be Moufang. We also examine a class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. In particular, we consider closure properties of certain extensions similar to those as in [S. Gagola III, Cyclic extensions of Moufang loops induced by semiautomorphisms,...

Currently displaying 1 – 16 of 16

Page 1

Displaying 1 – 16 of 16

Medial division groupoids

Medial quasigroups of prime square order

Medial quasigroups of type $(n, k)$

Minimally nonassociative Moufang loops with a unique nonidentity commutator are ring alternative

Moufang loops arising from Zorn vector matrix algebras

Moufang loops of odd order $p_{1} p_{2} \dots p_{n} q^{3}$ .

Moufang loops of odd order $p_{1} p_{2} \dots p_{n} q^{3}$ with non-trivial nucleus

Moufang loops of order 243

Moufang loops of order coprime to three that cyclically extend groups of dihedral type

Moufang semidirect products of loops with groups and inverse property extensions

Multiplication groups of free loops. I

Multiplication groups of free loops. II

Multiplication groups of quasigroups and loops I.

Multiplication groups of quasigroups and loops II.

Multiplication groups of quasigroups and loops III.

Multiplication groups of quasigroups and loops IV.

Currently displaying 1 – 16 of 16