What are the elements of the subgroups <3> and <15> in Z(18)?

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SUMMARY

The elements of the subgroups <3> and <15> in Z(18) are definitively identified as follows: <3> consists of the elements {0, 3, 6, 9, 12, 15}, while <15> contains the elements {0, 15}. The total number of unique elements across both subgroups is 7, although <15> is noted to have fewer distinct elements than initially suggested. This analysis confirms the subgroup structures within the additive group Z(18).

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Homework Statement



List the elements of the subgroups <3> abd <15> in Z(18)


Homework Equations





The Attempt at a Solution



<3>={0,3,6,9,12,15} .
<15> ={0,15}

Together , I can conclude that the number of elements amongst <3> and <15> add up to 7 elements.
 
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It's all correct, although I'm not sure that:
Benzoate said:
Together , I can conclude that the number of elements amongst <3> and <15> add up to 7 elements.
Is all that interesting.
 
Benzoate said:
<15> ={0,15}

<15> has more elements than that.
 

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