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Chapter 4:  
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== Homework solutions ==
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Problem 9
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* HW 1 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/1.txt]]
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From theorem 4.3 we know that "for each positive divisor k of n, the group <a> has exactly one subgroup of order k"  ==> <a^(n/k)> 
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* HW 2 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/2.txt]]
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* HW 3 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/3.txt]]
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* HW 4 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/4.txt]]
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* HW 5 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/5.txt]]
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* HW 6 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/6.txt]]
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* HW 7 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/7.txt]]
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* HW 8 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/8.txt]]
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* HW 9 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/9.txt]]
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* HW 10 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/10.txt]]
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* HW 11 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/11.txt]]
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* HW 12 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/12.txt]]
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* HW 13 is in [[http://www.math.purdue.edu/~walther/teach/453/hw/13.txt]]
  
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"For each positive divisor k of n, the set <n/k> is the unique subgroup of Zn of order k. Most importantly these are the only subgroups of Zn."
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[[Chapter 4: Problem 9 MA 453 Fall 2012]]
  
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Therefore if we follow the similiar examples on page 78 and 79 (example 5) we can see that for each divisor k of 20, the set <20/k> is the unique subgroup of Z20 of order k and are the only subgroups of Z20.
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[[Hw 7]]
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Thus <1>, <2>, <4>, <5>, <10> and <20> are the subgroups of Z20.
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Similarily, from the example on page 78 we see that <a>, <a^2>  , <a^4>, <a^5>, <a^10>, <a^20> are the subgroups of G.
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[[Hw 9]]
  
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The generators are just the divisors of 20 (for Z20) or are a^k with k being a divisor of 20 (for the set G).
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[[Last homework, MA453]]
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==> 1 , 2 , 4, 5, 10, 20
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==> a, a^2, a^4, a^5, a^10, a^20
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== Homework solutions ==
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I know it's rather late, by I feel that it would be good review to discuss some of the homework problems. So here are some of the past homework problems and some solutions. Feel free to enter in any unanswered questions. --[[User:Bakey|Bakey]] 11:26, 6 December 2012 (UTC)
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* HW 1 is in [[www.math.purdue.edu/~walther]]
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[[Chapters 12 and 13, MA 453]]
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[[Chapters 14 and 15, MA 453]]
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[[Chapters 16, MA 453]]
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[[Chapters 17, MA 453]]

Latest revision as of 05:20, 10 December 2012

Homework solutions

  • HW 1 is in [[1]]
  • HW 2 is in [[2]]
  • HW 3 is in [[3]]
  • HW 4 is in [[4]]
  • HW 5 is in [[5]]
  • HW 6 is in [[6]]
  • HW 7 is in [[7]]
  • HW 8 is in [[8]]
  • HW 9 is in [[9]]
  • HW 10 is in [[10]]
  • HW 11 is in [[11]]
  • HW 12 is in [[12]]
  • HW 13 is in [[13]]

Chapter 4: Problem 9 MA 453 Fall 2012

Hw 7

Hw 9

Last homework, MA453

I know it's rather late, by I feel that it would be good review to discuss some of the homework problems. So here are some of the past homework problems and some solutions. Feel free to enter in any unanswered questions. --Bakey 11:26, 6 December 2012 (UTC)


Chapters 12 and 13, MA 453

Chapters 14 and 15, MA 453

Chapters 16, MA 453

Chapters 17, MA 453

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