  positive integer? State the general result.16. Find a collection of distinct subgroups (a), (a2),..., (a of Z40with the property that (a) C (a)C..C (a with n as large aspossible.= la2l if and only if lal..17. Complete the following statement: lal

Question

16 help_outlineImage Transcriptionclosepositive integer? State the general result. 16. Find a collection of distinct subgroups (a), (a2),..., (a of Z40 with the property that (a) C (a)C..C (a with n as large as possible. = la2l if and only if lal.. 17. Complete the following statement: lal fullscreen
Step 1

It is known that in the group Zn , if  d divides n , then Zn has a unique subgroup of order d and that subgroup is  <n/d> .

Step 2

Since, the divisors of 240 are {1,2,3,4,5,6,……80,120,240},

Therefore, collection of subgroups of Z240 will be:

<0> = <0>

<120> is a subgroup of order 2.

<80> is a subgroup of order 3.

<60> is a subgroup of order 4.

….          ...

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