5. Quotient Groups

Question 1

Normal Subgroup

Answer 1

A subgroup where it is normal under conjugation: xHx^-1=H or xH=Hx

Question 2

Normaliser

Answer 2

The set of elements that satisfy the condition of being normal under conjugation

Question 3

Subgroup of index 2

Answer 3

Example of a NORMAL subgroup!

Question 4

Quotient Group

Answer 4

Suppose H is a normal subgroup of a group G. Then the Quotient group is the set G/H of left cosets of H.

Question 5

Quotient Map from G to G/H

Answer 5

Let H be a normal subgroup of a group G. The group homomorphism sending g∈G to its coset gH

Question 6

Order of Quotient Group

Answer 6

|G|/|H|