{"id":1127,"date":"2015-02-02T22:23:57","date_gmt":"2015-02-03T03:23:57","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/fgarvan\/?page_id=1127"},"modified":"2026-03-19T08:11:14","modified_gmt":"2026-03-19T12:11:14","slug":"sughw","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/fgarvan\/teaching\/absalg\/sughw\/","title":{"rendered":"Suggested Homework"},"content":{"rendered":"\r\n
\r\n\t
\r\n\t\t
\r\n\t\t\t
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Suggested Homework<\/h1>\n\n\n\n

\nEDITION 9 SUGGESTED PROBLEMS
\n<\/p>\n\n\n\n


    \n
  • Chapter 1 – Introduction to Groups

    \n 2, 13
    \n<\/li>
  • Chapter 2 – Groups

    \n 5, 20, 22, 26, 30, 32, 34, 41, 42, 43, 44
    \n<\/li>
  • Chapter 3 – Finite Groups, Subgroups

    \n 1, 7, 19, 21, 23, 35, 47, 51, 53, 54, 59
    \n<\/li>
  • Chapter 4 – Cyclic Groups

    \n 2, 4, 8, 16, 26, 62
    \n<\/li>
  • Chapter 5 – Permutation Groups

    \n 1, 2, 3, 4, 5, 6, 7, 15, 29, 37, 43, 55
    \n<\/li>
  • Chapter 6 \u2013 Isomorphisms

    \n 1, 5, 7, 13, 29, 39, 56, 65
    \n This problem in 8th edition but not 9th:
    \n Let a be belong to a group G and let |a| be finite. Let phia<\/sub> be the automorphism of G given by phia<\/sub>(x) = a x a-1<\/sup>. Show that |phia<\/sub>| divides |a|. Exhibit an element a from a group for which 1 lt |phia<\/sub>| lt |a|.
    \n<\/li>
  • Chapter 7 \u2013 Cosets and Lagrange\u2019s Theorem

    \n 1, 5, 7, 9, 17, 21, 27, 29, 47
    \n<\/li>
  • Chapter 8 \u2013 External Direct Products

    \n 5, 7, 11, 17, 22, 50, 69
    \nThis problem is in 8thedition but not 9th:
    \n Is Z3<\/sub>+Z5<\/sub> isomorphic to Z15<\/sub>? Why?
    \n<\/li>
  • Chapter 9 – Normal Subgroups and Factor Groups

    \n 10, 11, 12, 14, 25, 28, 34, 48, 50, 70
    \n<\/li>
  • Chapter 10 – Group Homomorphisms

    \n 7, 9, 13, 14, 15, 16, 17, 18, 19, 21, 25
    \n<\/li>
  • Chapter 11 – Fundamental Theorem of Finite Abelian Groups

    \n 6, 7, 8, 9, 10, 21, 26, 27
    \n<\/li>
  • Chapter 12 – Introduction to Rings

    \n 2, 6, 13, 23, 32, 50
    \n<\/li>
  • Chapter 13 – Integral Domains

    \n TBA
    \n<\/li><\/ul>\n\n\n\n

    \nEDITION 8 SUGGESTED PROBLEMS
    \n<\/p>\n\n\n\n


      \n
    • Chapter 1 – Introduction to Groups

      \n 2, 11
      \n<\/li>
    • Chapter 2 – Groups

      \n 5, 20, 22, 26, 30, 32, 34, 41, 42, 43, 44
      \n<\/li>
    • Chapter 3 – Finite Groups, Subgroups

      \n 1, 7, 12, 19, 21, 23, 33, 45, 48, 51, 53, 54, 61
      \n<\/li>
    • Chapter 4 – Cyclic Groups

      \n 2, 4, 8, 16, 17, 26, 64
      \n<\/li>
    • Chapter 5 – Permutation Groups

      \n 1, 2, 3, 4, 5, 6, 7, 15, 29, 37, 45, 71
      \n<\/li>
    • Chapter 6 \u2013 Isomorphisms

      \n 1, 5, 7, 11, 27, 37, 53, 54, 61
      \n<\/li>
    • Chapter 7 \u2013 Cosets and Lagrange\u2019s Theorem

      \n 1, 3, 7, 9, 17, 21, 27, 29, 47
      \n<\/li>
    • Chapter 8 \u2013 External Direct Products

      \n 5, 7, 9, 11, 17, 22, 53, 73
      \n<\/li>
    • Chapter 9 – Normal Subgroups and Factor Groups

      \n 11, 12, 13, 14, 28, 32, 34, 48, 50, 72
      \n<\/li>
    • Chapter 10 – Group Homomorphisms

      \n 7, 9, 13, 14, 15, 16, 17, 18, 19, 21, 25
      \n<\/li>
    • Chapter 11 – Fundamental Theorem of Finite Abelian Groups

      \n 6, 7, 8, 9, 10, 21, 26, 27
      \n<\/li>
    • Chapter 12 – Introduction to Rings

      \n 2, 6, 13, 23, 32, 50
      \n<\/li>
    • Chapter 13 – Integral Domains

      \n 15, 24, 35, 41, 42, 46
      \n<\/li><\/ul>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":140,"featured_media":0,"parent":1042,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1127","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages\/1127","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/users\/140"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/comments?post=1127"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages\/1127\/revisions"}],"predecessor-version":[{"id":3468,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages\/1127\/revisions\/3468"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages\/1042"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/media?parent=1127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}