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Find all subgroups of order 4 in Z4 Z4.

Chapter 8, Problem 30E

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QUESTION:

Find all subgroups of order 4 in Z4 ? Z4.

Questions & Answers

QUESTION:

Find all subgroups of order 4 in Z4 ? Z4.

ANSWER:

Step 1 of 4

Consider that  will always be Abelian. So only two possibilities are there for a subgroup of order .

Consider the first possibility,

                                                                       

Here,  is an element of , of order .

The values  and  be such that ,

                                                                       

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