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An infinite cyclic group does not have a ______ series.

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An infinite cyclic group does not have a ______ series.

(a) AP

(b) GP

(c) Composite

(d) Finite

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Question is taken from Cyclic Groups topic in chapter Groups of Discrete Mathematics

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Correct choice is (c) Composite

To elaborate: Suppose that any finite group of order less than n has a composition series. Let G be a finite group of order n. If G is simple, then G⊳{e}, where e is the identity element of G and hence, it is a composition series. However, any infinite cyclic group does not have a composite series.

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