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    ON MULTIPLICATION GROUPS OF ISOSTROPHIC QUASIGROUPS.
    (Valines SRL, 2014) Grecu, Ion
    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.