Displaying similar documents to “Loop characters”

The upper triangular algebra loop of degree 4

Kenneth Walter Johnson, M. Munywoki, Jonathan D. H. Smith (2014)

Commentationes Mathematicae Universitatis Carolinae

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A natural loop structure is defined on the set U 4 of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A detailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.

Nonsplitting F-quasigroups

Stephen Gagola III (2012)

Commentationes Mathematicae Universitatis Carolinae

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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

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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.