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Let Z denote the group of integers under addition. Is

Chapter 4, Problem 23E

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QUESTION:

Problem 23E

Let Z denote the group of integers under addition. Is every subgroup of Z cyclic? Why? Describe all the subgroups of Z. Let a be a group element with infinite order. Describe all subgroups of

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QUESTION:

Problem 23E

Let Z denote the group of integers under addition. Is every subgroup of Z cyclic? Why? Describe all the subgroups of Z. Let a be a group element with infinite order. Describe all subgroups of

ANSWER:

Step 1 of 3

It is known that every subgroup of a cyclic group is cyclic. Also,  is cyclic for addition which is also a subgroup of . Hence,  is a cyclic group and all its subgroups are also cyclic.

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