Nonsplitting F-quasigroups

Stephen Gagola III

Commentationes Mathematicae Universitatis Carolinae (2012)

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

Abstract

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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 nonsplit NK-loops of minimal order 3 6 .

How to cite

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Gagola 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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