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Quasigroups of transformations. (English) Zbl 0812.22004
Lómus, J. (ed.) et al., Quasigroups and nonassociative algebras in physics. Papers from the seminar held in Tartu (USSR), June 12-17, 1989. Tartu: Institut Fiziki AN Ehstonii, Eesti Teaduste Akadeemia Füüsika Instituudi Uurimused. 66, 54-66 (1990).
Summary: The work deals with the families of transformations of a set (a smooth manifold) $$M$$, which are not necessarily closed with respect to the composition law. In this case the system of notions of the theory of quasigroups and loops appears to be a natural working language, since the action of a family of transformations with regard to an arbitrary fixed point $$a$$ of the set $$M$$ can be described by a loop; loops associated with different points of the set $$M$$ are isotopic to each other. The construction was meant for applications in geometry and mathematical physics.
For the entire collection see [Zbl 0788.00016].

##### MSC:
 22A30 Other topological algebraic systems and their representations 20N05 Loops, quasigroups 57S99 Topological transformation groups
##### Keywords:
smooth manifold; quasigroups; loops; transformations