# Quasigroup

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## Definition of the noun Quasigroup

What does Quasigroup mean as a name of something?

**noun**

- [
*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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## Video about Quasigroup

**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 Q_{10}U_{1}A_{1}S_{1}I_{1}G_{2}R_{1}O_{1}U_{1}P_{3}

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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