On the theory of left F-quasigroups

Three main results concerning the left F-quasigroups and their canonical loopuscular structures are proved. First, it is shown that the canonical loopuscular structure of the left F-quasigroup is reductive (Proposition 2). Second, it is proved that canonical loopuscular structures of the left F-quasigroups are invariant with regard to right isotopes (Proposition 2). Finally, necessary and sufficient conditions for a loop to be represented using the canonical loopuscular structure of some left F-quasigroup are formulated, and a method of reconstruction of a left F-quasigroup from its canonical loopuscular structure is described (Proposition 3). For details the reader should consult the paper itself.