Spring 2002 Math 3321 Review Test # 3

Dr. Cordero

  1. Define <a, b>.
  2. Define A X B for A and B groups.
  3. Ha=Hb is equivalent to … (in other words, state Lemma 16.1)
  4. State and proof Lagrange’s Theorem
  5. Give three corollaries to Lagrange’s Theorem
  6. State Theorem 17.1
  7. Give the lattice of subgroups of 
  8. Define isomorphism
  9. State and proof Theorem 18.2
  10. State Theorem 19.1
  11. Give the number of isomorphism classes of groups of order n:
    • If n=p, p prime
    • If n=, p prime
    •  such that  does not divide  for all i, j.
  12. State the Fundamental Theorem of Abelian Groups
  13. State and proof Cayley’s Theorem.
  14. Define group homomorphism.
  15. Define kernel of a homomorphism.
  16. State and proof Theorem 21.1