(New page: Category:MA453Spring2009Walther I solved this one by using the same process we used in class with Z_48. Find the divisors of 20 to find each subgroup, then figure out how to generate...) |
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I solved this one by using the same process we used in class with Z_48. Find the divisors of 20 to find each subgroup, then figure out how to generate the subgroup based on its structure. | I solved this one by using the same process we used in class with Z_48. Find the divisors of 20 to find each subgroup, then figure out how to generate the subgroup based on its structure. | ||
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| + | I think <math>Z_{20}</math> has 6 subgroups, generated by <math>\overline{0}</math>, <math>\overline{1}</math>, <math>\overline{2}</math>, <math>\overline{4}</math>, <math>\overline{5}</math>, and <math>\overline{10}</math>. For the second part of the question, ''G'' also has 6 subgroups, this time generated by <math>\overline{0}, \overline{a}, \overline{2a}, \overline{4a}, \overline{5a},</math> and <math>\overline{10a}</math>. Does this seem right? | ||
Revision as of 18:48, 4 February 2009
I solved this one by using the same process we used in class with Z_48. Find the divisors of 20 to find each subgroup, then figure out how to generate the subgroup based on its structure.
I think $ Z_{20} $ has 6 subgroups, generated by $ \overline{0} $, $ \overline{1} $, $ \overline{2} $, $ \overline{4} $, $ \overline{5} $, and $ \overline{10} $. For the second part of the question, G also has 6 subgroups, this time generated by $ \overline{0}, \overline{a}, \overline{2a}, \overline{4a}, \overline{5a}, $ and $ \overline{10a} $. Does this seem right?
