# What does the term abelian mean?

The term *abelian* is most commonly encountered in group
theory, where it refers to a specific type of group known as an
*abelian group*. An abelian group, simply put, is a
commutative group, meaning that when the group operation is applied
to two elements of the group, the order of the elements doesn't
matter.

For example:

Let *G* be a group with multiplication * or addition +. If,
for any two elements *a*, *b* Є *G*,
*a***b* = *b***a* or *a* + *b* =
*b* + *a*, then we call the group abelian.

There are other uses of the term abelian in other fields of math, and most of the time, the idea of commutativity is involved.

The term is named after the mathematician, Niels Abel.

### Is every abelian group is cyclic or not and why?

every abelian group is not cyclic. e.g, set of (Q,+) it is an abelian group but not cyclic.

### Is the symmetry group of the square an abelian group?

Abelian meaning commutative. If the symmetry group of a square is commutative then it's an abelian group or else it's not.

### What is Abelian algebra?

Abelian algebra is a form of algebra in which the multiplication within an expression is commutative.

### Is a group of order 24 abelian group or not?

The abelian groups of order 24 are C3xC8, C2xC12, C2xC2xC6. There are other 12 non-abelian groups of order 24

### What is the definition of an abelian group?

An abelian group is a group in which ab = ba for all members a and b of the group.

### Is every finite abelian group is cyclic?

No, for instance the Klein group is finite and abelian but not cyclic. Even more groups can be found having this chariacteristic for instance Z9 x Z9 is abelian but not cyclic

### What is an Abelian group?

a group or set of group is said to be abelian if the law of commutation is always held. it means if for a group or set S having elements a,b belongs to S then a*b=b*a then the group is called abelian group.

### What has the author A P Mishina written?

A. P. Mishina has written: 'Higher algebra' 'Abelian groups and modules' -- subject(s): Abelian groups, Modules (Algebra)

### What has the author H Inassaridze written?

H. Inassaridze has written: 'Non-Abelian homological algebra and its applications' -- subject(s): Algebra, Homological, Homological Algebra, Non-Abelian groups

### What has the author Francis Borceux written?

Francis Borceux has written: 'Mal'cev, protomodular, homological and semi-abelian categories' -- subject(s): Abelian categories, Categories (Mathematics), Homological Algebra

### What is abelianization?

Abelianization is a homomorphism which transforms a group into an Abelian group.

### What is the mathamatical term for mean?

The mathematical term for "mean" is "mean". The popular, or colloquial term for "mean" is "average".

### What has the author Christina Birkenhake written?

Christina Birkenhake has written: 'Complex Abelian varieties' -- subject(s): Abelian varieties, Riemann surfaces 'Complex tori' -- subject(s): Complex manifolds, Torus (Geometry)

### What has the author Henry Frederick Baker written?

Henry Frederick Baker has written: 'Abel's theorem and the allied theory' -- subject(s): Abelian Functions, Functions, Abelian, Functions, Theta, Riemann surfaces, Theta Functions

### What is a generalization for 3x5 equals 5x3?

The generalisation is that multiplication is Abelian (or commutative) for numbers.

### What is the property of 5xp equals px5?

The Abelian or commutative property of multiplication of numbers.

### What has the author Bernard Kin-sion Cheung written?

Bernard Kin-sion Cheung has written: 'On the structure of multiplicative cohomology theory with abelian coefficients' -- subject(s): Abelian groups, Homology theory, Homotopy theory

### What does term invaders mean?

term invaders mean i do not know hahahaahhaahhahahahahahahhahahahahahahah

### Computer terms GB MB MHz KB bytes smallest to the largest?

the term GB what does it mean the term MB what does it mean the term MHz what does it mean the term KB what does it mean the term bytes what does it mean ? i see the terms on my computer and i would like the defnition of each one.

### Pq plus qp?

If you are working with real numbers, or even complex numbers, pq is the same as qp, so the result is the same as 2pq. If you use some multiplication that is NOT commutative (such as, when you multiply matrices), you can't simplify the expression.

### What is abelianness?

Abelianness is the quality of an expression being abelian - having a commutative-defining operation.

### What is the number of groups of order 8 upto isomorphisms?

There are 5 groups of order 8 up to isomorphism. 3 abelian ones (C8, C4xC2, C2xC2xC2) and 2 non-abelian ones (dihedral group D8 and quaternion group Q)

### Prove that a group of order three is abelian?

By LaGrange's Thm., the order of an element of a group must divide the order of the group. Since 3 is prime, up to isomorphism, the only group of order three is {1,x,x^2} where x^3=1. Note that this is a finite cyclic group. Since all cyclic groups are abelian, because they can be modeled by addition mod an integer, the group of order 3 is abelian.

### What does the term putting together in algebra mean?

what does the term putting together mean

### Changing the order of the addends or factors represent what property of math?

Commutative property or Abelian property.

### What has the author Joel Samuel Georges written?

Joel Samuel Georges has written: 'Associativity conditions for division algebras corresponding to any Abelian group' -- subject(s): Abelian groups, Universal Algebra 'Introductory mathematical analysis' -- subject(s): Calculus, Functions

### What does the term other hearing mean in court?

what does the term "other hearing" mean in the court of law

### What does TTO shipping term mean?

It is presumed to mean, "Tanker Take Over." Though there is no such term.

### What has the author La szlo Fuchs written?

La szlo . Fuchs has written: 'Infinite Abelian groups'

### What is the property of 9 times 7 equals 7 times 9?

Commutativity (or Abelian) property of multiplication.

### How many abelian groups up to isomorphism are there of order 32?

7 groups, use the structure theorem