ON MULTIPLICATION GROUPS OF ISOSTROPHIC QUASIGROUPS.
Date
2014
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Valines SRL
Abstract
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.
Description
Keywords
Right (left, middle) Bol loop, isostrophy, (right, left) multiplication group.
Citation
GRECU, I. On multiplication groups of isostrophic quasigroups. In: The Third Conference of Mathematical Society of the Republic of Moldova: dedicated to the 50th anniversary of the foundation of the Institute of Mathematics and Computer Science, 19-23 aug. 2014, Chisinau, Moldova: Proceedings IMCS-50.Ch., 2014, pp.78-81. ISBN 978-9975-68-244-2