Commutants of middle Bol loops
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2020-11-01 21:01
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GRECU, Ion, SYRBU, Parascovia. Commutants of middle Bol loops. In: Quasigroups and Related Systems, 2014, vol. 22, nr. 1(31), pp. 81-88. ISSN 1561-2848.
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Quasigroups and Related Systems
Volumul 22, Numărul 1(31) / 2014 / ISSN 1561-2848

Commutants of middle Bol loops

Pag. 81-88

Grecu Ion, Syrbu Parascovia
 
Moldova State University
 
 
Disponibil în IBN: 30 septembrie 2014


Rezumat

The commutant of a loop is the set of all its elements that commute with each element of the loop. It is known that the commutant of a left or right Bol loop is not a subloop in general. Below we prove that the commutant of a middle Bol loop is an AIP-subloop, i.e., a subloop for which the inversion is an automorphism. A necessary and sucient condition when the commutant is invariant under the existing isostrophy between middle Bol loops and the corresponding right Bol loops is given.