MTH633 Practice Questions Lectures 23-25 Modules 90-101 by VUBuddy

Practice Questions · MTH633 · Lectures ( 23 – 25 ) or Modules ( 90 – 101 )

Q1. What is Factor or quotient group? Give an example.

Q2. State and explain first isomorphism theorem.

Q3. Let ( G, . ) be a group with subgroup H. For

a b G what do you mean by a congruent to b modulo H?

Q4. Write down Two normal subgroups of 

1, 1, , i i j j k k

Q5. Define kernel of homomorphism, and give an example.

Q6. Let y be the natural map of Z into Z

n given by y(m) = r, where r is the remainder given by the division algorithm when m is divided by n. Show that y is a homomorphism. Find Ker(y).