Quasigroups

DOI10.1007/BF02133175zbMath0697.20050OpenAlexW4211114482MaRDI QIDQ910866

V. M. Galkin

Publication date: 1990

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02133175

zbMATH Keywords

surveyMoufang loopsBol loopsinverse property loopsleft distributive quasigroups

Mathematics Subject Classification ID

Loops, quasigroups (20N05)

Related Items (4)

Connected quandles and transitive groups ⋮ Selected group-theoretic aspects of confirmation measure symmetries ⋮ Nonaffine latin quandles of order 2k ⋮ The torsion of a finite quasigroup quandle is annihilated by its order

Cites Work

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• On self-adjoint subloops of moufang loops
• Quasidirect products of quasigroups
• Finite distributive quasigroups
• Left Loops which Satisfy the Left Bol Identity
• Inverse-Cycles in Weak-Inverse Loops
• A special embedding of Bol loops in groups
• Moufang loops of small order
• Construction of commutative weak inverse property loops of most orders
• Stein quasigroups I: Combinatorial aspects
• Simple Moufang loops
• ON WEAK ASSOCIATIVE LAWS IN COMMUTATIVE IP-LOOPS
• Finite Bol loops
• Structure of weakly abelian quasigroups
• On the nilpotence class of commutative Moufang loops
• A second grammar of associators
• A Generalization of a Theorem of Belousov
• ON INVERSE PROPERTY LOOPS
• Quasigroups determined by balanced identities of length $\leqq6$
• ON SCHREIER EXTENSION OF LOOPS
• Quelques consequences de la locale nilpotence des boucles de moufang commutatives
• Moufang Loops of Small Order. I
• Finite Bol loops: III
• Principal Loop-Isotopes of Quasigroups
• A Class of Loops with the Isotopy-Isomorphy Property
• Quasigroupes demi‐symétriques. Isotopies préservant la demi‐symétrie
• Inverse Loops as Groupoids with One Law
• When Is a Totally Symmetric Loop a Group?
• The Generalized Singular Direct Product for Quasigroups
• Construction of Quasigroups Satisfying the Identity X(XY) = YX
• An "Extra" Law for Characterizing Moufang Loops
• Integrally Closed and Complete Ordered Quasigroups and Loops
• Construction of Quasigroups Using the Singular Direct Product
• A Special Class of Moufang Loops
• On Weak Inverse Property Loops
• On one class of quasigroups
• Hall triple systems and commutative Moufang exponent 3 loops: The case of nilpotence class 2
• Characters of finite quasigroups
• On multiplication groups of quasigroups
• 3-Abelian groups and commutative Moufang loops
• On affine planes over \(A_n^k\)-quasigroups
• Sylow properties of a class of quasigroups
• A class of non-Moufang Bol loops isomorphic to all their loop isotopes
• A remark on commutative di-associative loops
• Differenzierbare distributive Quasigruppen
• On the construction of Schroeder quasigroups
• Free commutative Moufang loops and anticommutative graded rings
• Analytic Moufang loops in the large
• Bol loops of order \(p^ n\) (\(n\geq 3\), \(p\geq 2\))
• Self-orthogonal semisymmetric quasigroups
• Commutative Moufang loops and Bessel functions
• On the number of conjugates of a quasigroup
• Construction of n-cyclic quasi-groups and applications
• Examples of some quasigroups and loops admitting only discrete topologization
• The smallest non-derived Steiner triple system is simple as a loop
• Conjugate orthogonal quasigroups
• A short note on supernuclear (central) elements of inverse property loops
• L'irreductibilité centrale dans les boucles de Moufang commutatives et dans les systèmes triples de Hall
• Isotopy-isomorphy loops of prime order
• A note on loops
• On loops of odd order. II
• Nilpotence of finite Moufang 2-loops
• On the multiplication group of a loop
• Lattice-ordered loops and quasigroups
• Construction \(A_ n^ k\)-algebras
• On maps \(x \to x^ n\) and the isotopy-isomorphy property of Moufang loops
• Concerning ordered loops
• Systems of convex subloops of linearly ordered loops
• The smallest Moufang loop
• Induced topologies for quasigroups and loops
• Construction of Steiner quasigroups containing a specified number of subquasigroups of a given order
• Lagrange's theorem for M\(_k\)-loops
• On loops of odd order
• Stein quasigroups II: algebraic aspects
• On the spectrum of Stein quasigroups
• Commutative Moufang loops and distributive groupoids of small orders
• On symmetric quasigroups
• The Akivis algebra of a homogeneous loop
• On Quotient Loops of Normal Subloops
• $F$-quasigroups isotopic to Moufang loops
• Finite Bol loops II
• Bol loops of order pq
• A Class of Loops Which are Isomorphic to all Loop Isotopes
• Ordre minimum des boucles de Moufang commutatives de classe 2 (Resp. 3)

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