Results for: Abelians

In Math and Arithmetic

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) (MORE)
In Math and Arithmetic

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 (MORE)
In Math and Arithmetic

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} wher (MORE)
In Math and Arithmetic

Show that the set of all real numbers is an abelian group with respect to addition?

Let R represent the set of real numbers. Then Closure For all x and y in R , x+y belongs to R . Associativity For all x, y and z in R , (x + y) + z = x + (y + z). I (MORE)
In Math and Arithmetic

Is every cyclic group abelian?

Yes. Lets call the generator of the group z, then every element of the group can be written as z k for some k. Then the product of two elements is: z k z m =z k+m Notice (MORE)
In Topology

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 co (MORE)
In Definitions

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 t (MORE)
In Definitions

What is Abelian algebra?

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