### Abstract

the aim of this paper is to prove that a quasigroup Q with right unit is isomorphic to an f-extension of a right nuclear normal subgroup G by the factor quasigroup Q/G if and only if there exists a normalized left transversal ∑ ⊂ Q to G in Q such that the right translations by elements of ∑ commute with all right translations by elements of the subgroup G. Moreover, a loop Q is isomorphic to an f-extension of a right nuclear normal subgroup G by a loop if and only if G is middle-nuclear, and there exists a normalized left transversal to G in Q contained in the commutant of G.

Original language | English (US) |
---|---|

Pages (from-to) | 391-395 |

Number of pages | 5 |

Journal | Commentationes Mathematicae Universitatis Carolinae |

Volume | 53 |

Issue number | 3 |

State | Published - Dec 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Commentationes Mathematicae Universitatis Carolinae*,

*53*(3), 391-395.

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*Commentationes Mathematicae Universitatis Carolinae*, vol. 53, no. 3, pp. 391-395.

**Quasigroups arisen by right nuclear extension.** / Nagy, Peter T.; Stuhl, Izabella.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quasigroups arisen by right nuclear extension

AU - Nagy, Peter T.

AU - Stuhl, Izabella

PY - 2012/12/1

Y1 - 2012/12/1

N2 - the aim of this paper is to prove that a quasigroup Q with right unit is isomorphic to an f-extension of a right nuclear normal subgroup G by the factor quasigroup Q/G if and only if there exists a normalized left transversal ∑ ⊂ Q to G in Q such that the right translations by elements of ∑ commute with all right translations by elements of the subgroup G. Moreover, a loop Q is isomorphic to an f-extension of a right nuclear normal subgroup G by a loop if and only if G is middle-nuclear, and there exists a normalized left transversal to G in Q contained in the commutant of G.

AB - the aim of this paper is to prove that a quasigroup Q with right unit is isomorphic to an f-extension of a right nuclear normal subgroup G by the factor quasigroup Q/G if and only if there exists a normalized left transversal ∑ ⊂ Q to G in Q such that the right translations by elements of ∑ commute with all right translations by elements of the subgroup G. Moreover, a loop Q is isomorphic to an f-extension of a right nuclear normal subgroup G by a loop if and only if G is middle-nuclear, and there exists a normalized left transversal to G in Q contained in the commutant of G.

UR - http://www.scopus.com/inward/record.url?scp=84872806883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872806883&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84872806883

VL - 53

SP - 391

EP - 395

JO - Commentationes Mathematicae Universitatis Carolinae

JF - Commentationes Mathematicae Universitatis Carolinae

SN - 0010-2628

IS - 3

ER -