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# Quasigroup

## Definition of the noun Quasigroup

What does Quasigroup mean as a name of something?

noun

1. [mathematics] An algebraic structure, resembling a group, whose arithmetic may not be associative

## Explanation

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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### Quantum Mechanics of Non-Hamiltonian and Dissipative Systems (2008)

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.

### Information Security and Cryptology (2014)

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 ...

### Geometry and Algebra of Multidimensional Three-Webs (1992)

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#) ...

### Introduction to Combinatorics (2013)

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 ...

### Introduction to Combinatorics, Second Edition (2016)

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.

### Encyclopedia of Research Design (2010)

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 ...

### Encyclopedia of Social Theory (2004)

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 ...

### Encyclopedic Dictionary of Mathematics (1993)

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; ...

## Online dictionaries and encyclopedias with entries for Quasigroup

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Quasigroup Meaning

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.