## Results for: Abelian Group

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) ( Full Answer )
In Algebra

# 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.
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 ( Full Answer )
In Algebra

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

\nevery abelian group is not cyclic. e.g, set of (Q,+) it is an abelian group but not cyclic. \n
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 ( Full Answer )
In Algebra

# 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.
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 ( Full Answer )
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 ( Full Answer )
In Abstract Algebra

# 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
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 ( Full Answer )