ON MULTIPLICATION GROUPS OF ISOSTROPHIC QUASIGROUPS. - Grecu, Ion (Valines SRL, 2014)
Relations between the multiplication groups of loops which are isostrophes of quasigroups are studied in the present work. We prove that, if (Q; ¢) is a quasigroup and its isostrophe (Q; ±), where x ± y = Ã(y) n '(x), 8x; y 2 Q, is a loop, then the right multiplication group of (Q; ±) is a subgroup of the left multiplica- tion group of (Q; ¢). Moreover, if ' 2 Aut(Q; ±), then RM(Q; ±) is a normal subgroup of LM(Q; ¢). As a corollary from this result we get that the right multiplication group of a middle Bol loop coincides with the left multiplication group of the corresponding right Bol loop.
Keywords: Right (left, middle) Bol loop; isostrophy; (right, left) multiplication group.