# Results for: abelian group

### 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. Full Answer

### 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. Full Answer

### 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. Full Answer

### 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… Full Answer

### 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 Full Answer

No. Full Answer

No. Full Answer

### 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 Full Answer

### What is an abelianization?

An abelianization is a homomorphism which transforms a group into an abelian group. Full Answer

### What is abelianization?

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

### 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… Full Answer

### Example of group is an abelian group?

The set of integers, under addition. Full Answer

### 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… Full Answer

### What is a synonym for commutative property?

abelian group Full Answer

### What is an additive group?

An additive group is an abelian group when it is written using the + symbol for its binary operation. Full Answer

### What was the order of the 9 Chinese dynasties?

prove a group of order9 is abelian Full Answer

### 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) Full Answer

### 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)… Full Answer

### What is a bimodule?

A bimodule is an abelian group which is both a left and right module, such as the left and right multiplications are compatible. Full Answer

### When was Hovhannes Abelian born?

Hovhannes Abelian was born in 1865. Full Answer

### When did Hovhannes Abelian die?

Hovhannes Abelian died in 1936. Full Answer

### What is Abelian algebra?

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

### 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 Full Answer

### What has the author Paul Edwin Lewis written?

Paul Edwin Lewis has written: 'Characters of Abelian groups' -- subject(s): Group theory Full Answer

### What is an Abelian?

An Abelian is a member of a fourth-century African sect mentioned by St. Augsustine, who married but lived in continence. Full Answer

### What is another name for commutative property?

The Abelian property, after the Norwegian mathematician, Niels Abel (early 19th Century) who made major contributions to Group Theory. Full Answer

### 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) Full Answer

### What has the author A B Katok written?

A. B. Katok has written: 'Lectures on surfaces' -- subject(s): Surfaces 'Rigidity in higher rank Abelian group actions' -- subject(s): Rigidity (Geometry), Abelian groups 'Invariant manifolds, entropy, and billiards' -- subject(s): Entropy, Global analysis (Mathematics), Invariant manifolds, Ergodic theory, Differentiable… Full Answer

### 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 Full Answer

### 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 Full Answer

### Is every cyclic group abelian?

Yes. Lets call the generator of the group z, then every element of the group can be written as zk for some k. Then the product of two elements is: zkzm=zk+m Notice though that then zmzk=zm+k=zk+m=zkzm, so the group is… Full Answer

### Do matrices form an abelian group under multiplication?

More precisely, I think you're asking whether the set of n X n matrices forms an abelian group under multiplication. The answer is no (assuming n>1). For example (1 0)(0 1) = (0 1) (0 0)(0 0) (0 0), but… Full Answer

### What is a math property that starts with an a?

Abelian (meaning commutative: a + b = b + a). Full Answer

### What is purple and works from home?

A non-Abelian grape. (It doesn't commute.) Full Answer

### 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) Full Answer

### 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 Full Answer

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

The Abelian or commutative property of multiplication of numbers. Full Answer

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

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

### 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 Full Answer

### What is abelianness?

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

### What is an Abelonian?

An Abelonian is an alternative term for an Abelian - a member of a historical Roman Catholic sect. Full Answer

### Which property is A plus X equals X plus A?

The Abelian property or commutative property. Full Answer

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

Commutative property or Abelian property. Full Answer

### Which property does 21 plus 18 equals 18 plus 21?

Commutativity or Abelian property Full Answer

### What is the property of 3x plus 5y plus 5y plus 3x?

The Abelian property or commutativity. Full Answer