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Definition of the noun Quasigroup
What does Quasigroup mean as a name of something?
- [mathematics] An algebraic structure, resembling a group, whose arithmetic may not be associative
Quasigroup: In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative.
- also known as latin square, quasigroupe, Quasigruppe
Printed dictionaries and other books with definitions for Quasigroup
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by Vasily Tarasov
A quasigroup is a groupoid in which the equations AX = B, YA = B are uniquely solvable for arbitrary elements A and B. Let B\A be a solution of the equation AX = B, and let B/A be a solution of the equation YA = B. Then we can consider two ...
Combinatorial Designs (1989)
A Tribute to Haim Hanani by A. Hartman
Introduction A quasigroup is an ordered pair (Q, ), where Q is a set and (·) is a binary operation on Q such that the equations ax = b and ya = b are uniquely solvable for every pair of elements a, b in Q. It is fairly well-known (see, for example, ...
Alternative Loop Rings (1996)
by E.G. Goodaire, E. Jespers, C. Polcino Milies
A quasigroup is a pair (L, ) where L is a nonempty set and (a,b) → a b is a closed binary operation on L with the property that the equation a • b = c determines a unique 49 Chapter II. An Introduction to Loop Theory and to Moufang Loops 1.
9th International Conference, Inscrypt 2013, Guangzhou, China, November 27-30, 2013, Revised Selected Papers by Dongdai Lin, Shouhuai Xu, Moti Yung
Keywords: Stream cipher · Edon80 · Key-stream period · Quasigroup · Latin square 1 Introduction A quasigroup is an ordered pair (Q,∗), where Q is a set and ∗ is a binary operation on Q such that the equations a ∗ x = b and y ∗ a = b are ...
by M. Akivis, A.M. Shelekhov
12, the corresponding three-web is parallelizable, and its coordinate quasigroup is a commutative group. We arrive at the following proposition. Proposition 6.19 A Grassmann three-web W admits an (s + 1)- parameter group A#) ...
by Martin J. Erickson
A quasigroup is a groupoid such that given a, b E 8 there exist unique x, y with a * x = b and y * a = b. A loop is a quasigroup containing a two-sided identity e. The literature abounds with examples of these algebraic structures. For instance ...
by Walter D. Wallis, John C. George
An associative quasigroup is a semigroup and an associative loop is a group. Groups are widely studied objects, and most readers will be familiar with group theory. However, this significance is more algebraic than combinatorial.
by Neil J. Salkind
In mathematics, if the multiplication table of a binary function, say *, is a Latin square, then that function, together with the set of the elements, is called quasigroup. In contrast, if*is a binary function over the set S 1⁄4 f1;2;...;ng and satisfies the ...
by George Ritzer
Thus, the quasigroup as an aggregate of incumbents of positions with identical role interests represents the recruiting ground for an interest group ...
by Kiyosi Itô
—>ab which is not necessarily associative but satisfies the condition that any two among a, b, c in the equation ab=c determine the third uniquely, then Q is called a quasigroup.
Encyclopaedia of Mathematics (2013)
Volume 6: Subject Index — Author Index by Michiel Hazewinkel
Orthogonal Latin squares; Permanent; Quasigroup) (refers to: Cayley table, orthogonal Latin squares; ...
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Video about Quasigroup
Video shows what quasigroup means. An algebraic structure, resembling a group, whose arithmetic may not be associative. Quasigroup Meaning. How to ...
Scrabble value of Q10U1A1S1I1G2R1O1U1P3
The value of this 10-letter word is 22 points, but it's not an accepted word in the Official Scrabble Players Dictionary.
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