Necessary and sufficient condition for a finite group to be cyclic.
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- 27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. b. Show that a cyclic group of order has a cyclic group of order as a homomorphic image.True or False Label each of the following statements as either true or false. The order of an element of a finite group divides the order of the group.Lagranges Theorem states that the order of a subgroup of a finite group must divide the order of the group. Prove or disprove its converse: if k divides the order of a finite group G, then there must exist a subgroup of G having order k.