Suggested Homework


EDITION 9 SUGGESTED PROBLEMS

  • Chapter 1 – Introduction to Groups
    2, 13
  • Chapter 2 – Groups
    5, 20, 22, 26, 30, 32, 34, 41, 42, 43, 44
  • Chapter 3 – Finite Groups, Subgroups
    1, 7, 19, 21, 23, 35, 47, 51, 53, 54, 59
  • Chapter 4 – Cyclic Groups
    2, 4, 8, 16, 26, 62
  • Chapter 5 – Permutation Groups
    1, 2, 3, 4, 5, 6, 7, 15, 29, 37, 43, 55
  • Chapter 6 – Isomorphisms
    1, 5, 7, 13, 29, 39, 56, 65
    This problem in 8th edition but not 9th:
    Let a be belong to a group G and let |a| be finite. Let phia be the automorphism of G given by phia(x) = a x a-1. Show that |phia| divides |a|. Exhibit an element a from a group for which 1 lt |phia| lt |a|.
  • Chapter 7 – Cosets and Lagrange’s Theorem
    1, 5, 7, 9, 17, 21, 27, 29, 47
  • Chapter 8 – External Direct Products
    5, 7, 11, 17, 22, 50, 69
    This problem is in 8thedition but not 9th:
    Is Z3+Z5 isomorphic to Z15? Why?
  • Chapter 9 – Normal Subgroups and Factor Groups
    10, 11, 12, 14, 25, 28, 34, 48, 50, 70
  • Chapter 10 – Group Homomorphisms
    7, 9, 13, 14, 15, 16, 17, 18, 19, 21, 25
  • Chapter 11 – Fundamental Theorem of Finite Abelian Groups
    6, 7, 8, 9, 10, 21, 26, 27
  • Chapter 12 – Introduction to Rings
    2, 6, 13, 23, 32, 50
  • Chapter 13 – Integral Domains
    TBA


EDITION 8 SUGGESTED PROBLEMS

  • Chapter 1 – Introduction to Groups
    2, 11
  • Chapter 2 – Groups
    5, 20, 22, 26, 30, 32, 34, 41, 42, 43, 44
  • Chapter 3 – Finite Groups, Subgroups
    1, 7, 12, 19, 21, 23, 33, 45, 48, 51, 53, 54, 61
  • Chapter 4 – Cyclic Groups
    2, 4, 8, 16, 17, 26, 64
  • Chapter 5 – Permutation Groups
    1, 2, 3, 4, 5, 6, 7, 15, 29, 37, 45, 71
  • Chapter 6 – Isomorphisms
    1, 5, 7, 11, 27, 37, 53, 54, 61
  • Chapter 7 – Cosets and Lagrange’s Theorem
    1, 3, 7, 9, 17, 21, 27, 29, 47
  • Chapter 8 – External Direct Products
    5, 7, 9, 11, 17, 22, 53, 73
  • Chapter 9 – Normal Subgroups and Factor Groups
    11, 12, 13, 14, 28, 32, 34, 48, 50, 72
  • Chapter 10 – Group Homomorphisms
    7, 9, 13, 14, 15, 16, 17, 18, 19, 21, 25
  • Chapter 11 – Fundamental Theorem of Finite Abelian Groups
    6, 7, 8, 9, 10, 21, 26, 27
  • Chapter 12 – Introduction to Rings
    2, 6, 13, 23, 32, 50
  • Chapter 13 – Integral Domains
    15, 24, 35, 41, 42, 46