-
abstract algebra, a
quasigroup is an
algebraic structure that
resembles a
group in the
sense that "division" is
always possible.
Quasigroups differ from groups...
- with
quasigroups,
which are
generalization of
groups in a
different direction; the
operation in a
quasigroup need not be ****ociative but
quasigroups preserve...
- Şcerbacov,
Victor (2003). "Check
character systems over
quasigroups and loops" (PDF).
Quasigroups and
Related Systems. 10 (1): 1–28. ISSN 1561-2848. See...
- III,
Stephen (2011). "How and why
Moufang loops behave like groups".
Quasigroups and
Related Systems. 19: 1–22. Grishkov, Alexander; Zavarnitsine, Andrei...
- y) for all x, y in G. Such
quasigroups are said to be isotopic. If in the
above definition f = g = h then the
quasigroups are said to be isomorphic. Unlike...
- Bruck–Murdoch–Toyoda
theorem provides the
following characterization of
medial quasigroups.
Given an
abelian group A and two
commuting automorphisms φ and ψ of...
- one can
count to on one's
fingers using senary. 35 is the
number of
quasigroups of
order 4. 35 is the
smallest composite number of the form 6 k + 5 {\displaystyle...
-
quasigroups, loops, and non****ociative systems,
Denver 2005 Let ( Q , ∗ ) {\displaystyle (Q,*)} , ( Q , + ) {\displaystyle (Q,+)} be two
quasigroups defined...
- a CH-
quasigroup,
introduced by
Manin (1986,
definition 1.3), is a
symmetric quasigroup in
which any
three elements generate an
abelian quasigroup. "CH"...
- property.
Examples include matrix algebras,
quaternion algebras, and
quasigroups. In an
integral domain,
where not
every element need have an inverse...
