# Nonsplitting F-quasigroups

Commentationes Mathematicae Universitatis Carolinae (2012)

- Volume: 53, Issue: 3, page 375-381
- ISSN: 0010-2628

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topGagola III, Stephen. "Nonsplitting F-quasigroups." Commentationes Mathematicae Universitatis Carolinae 53.3 (2012): 375-381. <http://eudml.org/doc/247070>.

@article{GagolaIII2012,

abstract = {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 nonsplit NK-loops of minimal order $3^6$.},

author = {Gagola III, Stephen},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {F-quasigroup; NK-loop; Moufang loop; finite F-quasigroups; finite NK-loops; commutative Moufang loops},

language = {eng},

number = {3},

pages = {375-381},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Nonsplitting F-quasigroups},

url = {http://eudml.org/doc/247070},

volume = {53},

year = {2012},

}

TY - JOUR

AU - Gagola III, Stephen

TI - Nonsplitting F-quasigroups

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2012

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 53

IS - 3

SP - 375

EP - 381

AB - 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 nonsplit NK-loops of minimal order $3^6$.

LA - eng

KW - F-quasigroup; NK-loop; Moufang loop; finite F-quasigroups; finite NK-loops; commutative Moufang loops

UR - http://eudml.org/doc/247070

ER -

## References

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