### 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 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Quasigroups arisen by right nuclear extension'. Together they form a unique fingerprint.

## Cite this

Nagy, P. T., & Stuhl, I. (2012). Quasigroups arisen by right nuclear extension.

*Commentationes Mathematicae Universitatis Carolinae*,*53*(3), 391-395.