Displaying similar documents to “The upper triangular algebra loop of degree 4 ”

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...

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.