SOLUTION: Hi The Best Teachers online! Can you help me on this question please? Thank you! God bless! Find all subgroups of Z36 and draw the lattice diagram for the subgroups.

Z36 is the additive group of all integers from 0 to 35 modulus 36.


Its subgroups are:


1)  of the order 2:  {0,18};


2)  of the order 3:  {0,12,24};


3)  of the order 4:  {0,9,18,27};


4)  of the order 6:  {0,6,12,18,24,30};


5)  of the order 9:  {0,4,8,12,16,20,24,28,32};


6)  of the order 12:  {0,3,6,9,12,15,18,21,24,27,30,33};


7)  of the order 18:  {0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34}.