Quasigroups arisen by right nuclear extension

Peter T. Nagy, Izabella Stuhl

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)391-395
Number of pages5
JournalCommentationes Mathematicae Universitatis Carolinae
Volume53
Issue number3
StatePublished - Dec 1 2012

Fingerprint

Quasigroup
Normal subgroup
Isomorphic
If and only if
Commutant
Commute
Subgroup
Unit

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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

In: Commentationes Mathematicae Universitatis Carolinae, Vol. 53, No. 3, 01.12.2012, p. 391-395.

Research output: Contribution to journalArticle

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