The search session has expired. Please query the service again.

Displaying similar documents to “Multiplication groups of free loops. II”

On quasigroups with the left loop property

A. Nourou Issa (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.

Nonsplitting F-quasigroups

Stephen Gagola III (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

T. Kepka, M.K. Kinyon and J.D. Phillips: The structure of F-quasigroups, J. Algebra 317 (2007), no. 2, 435–461 developed a connection between F-quasigroups and NK-loops. Since NK-loops are contained in the variety generated by groups and commutative Moufang loops, a question that arises is whether or not there exists a nonsplit NK-loop and likewise a nonsplit F-quasigroup. Here we prove that there do indeed exist nonsplit F-quasigroups and show that there are exactly four corresponding...

Loops and quasigroups: Aspects of current work and prospects for the future

Jonathan D. H. Smith (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

This paper gives a brief survey of certain recently developing aspects of the study of loops and quasigroups, focussing on some of the areas that appear to exhibit the best prospects for subsequent research and for applications both inside and outside mathematics.