Abstract Algebra

What do you call the group when its cosets form a group?

• Coset Group

• Normal Subgroup

• Subgroup

• Quotient Group

Which of the following is the notation of Factor Group?

• G/N

• N

• 5Z

• 1 + 5Z

The composition of two homomorphisms is an automorphism. The truth value of this statement is

• TRUE

• FALSE

Quotient groups are also called

• Factor Groups

• Factor Subgroup

• Quotient Subgroup

• Division Group

In using the Cayley Table, what is the identity element if you are working with group operation addition for a group of integers?

• 0

• 1

• i

• -1

What are the two ways of comparing groups used in the presentation of homomorphism?

• Function and Relation

• Function and Cayley Table

• Relation and Cayley Table

• Isomorphism

Cosets always form a group. This statement is ________.

• True

• False

In comparing groups such as G and H, you should have a function f: G → H, where f(x⋅y)=f(x)⋅f(y). Operation in LHS is for the first group and the operation in the RHS is for the second group. They do not have to be the same. (I just cannot find a symbol appropriate from the formula option of the Quizizz.)

• True

• False

An isomorphism is a homomorphism that is one-to-one and onto.

• True

• False

The group of non-zero complex numbers is a Group under multiplication.

• True

• False