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.
