Explore: Quasigroups

abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible. Quasigroups differ from groups

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

with quasigroups, which are generalization of groups in a different direction; the operation in a quasigroup need not be associative but quasigroups preserve

quasigroups, loops, and nonassociative systems, Denver 2005 Let ( Q , ∗ ) {\displaystyle (Q,*)} , ( Q , + ) {\displaystyle (Q,+)} be two quasigroups defined

Bruck–Murdoch–Toyoda theorem provides the following characterization of medial quasigroups. Given an abelian group A and two commuting automorphisms φ and ψ of

Foundation. Sloane, N. J. A. (ed.). "Sequence A057771 (Number of loops (quasigroups with an identity element) of order n)". The On-Line Encyclopedia of Integer

a CH-quasigroup, introduced by Manin (1986, definition 1.3), is a symmetric quasigroup in which any three elements generate an abelian quasigroup. "CH"

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

ambient space, which carries one subset to the other Isotopy of quasigroups. See Quasigroup#Homotopy and isotopy. Isotopy of loops, a triple of maps with