Transversals in loops. 1. Elementary properties

Kuznetsov Eugene

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710

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2022-03-27 09:53

SM ISO690:2012

KUZNETSOV, Eugene. Transversals in loops. 1. Elementary properties. In: Quasigroups and Related Systems, 2010, vol. 18, nr. 1(23), pp. 43-58. ISSN 1561-2848.

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Quasigroups and Related Systems

Volumul 18, Numărul 1(23) / 2010 / ISSN 1561-2848

Transversals in loops. 1. Elementary properties

Pag. 43-58

Kuznetsov Eugene

Disponibil în IBN: 16 decembrie 2013

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A new notion of a transversal in a loop to its subloop is introduced and studied. This notion generalized a well-known notion of a transversal in a group to its subgroup and can be correctly dened only in the case, when some specic condition (condition A) for a loop and its subloop is fullled. Elementary properties of the transversals in a loop to its subloop are investigated and proved. With the help of the notion of transversal in a loop to its subloop a new notion of permutational representation of a loop by left (right) cosets to its subloop is introduced and studied.

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