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Exercise 14 Let G be a group. Which of the following statement(s) is/are true: I. If G is noncyclic, then there exists a proper non-cyclic subgroup of G. II. If a, b E G and Jal and |b| are finite, then Jab| is finite. III. NaeG C(a) = G if and only if G is abelian. (a) I and II only (b) II and III only OIII only (d) II only (e) I and III only

Exercise 14 Let G be a group. Which of the following statement(s) is/are true: I. If G is noncyclic, then there exists a proper non-cyclic subgroup of G. II. If a, b E G and Jal and |b| are finite, then Jab| is finite. III. NaeG C(a) = G if and only if G is abelian. (a) I and II only (b) II and III only OIII only (d) II only (e) I and III only

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 6TFE: True or false Label each of the following statements as either true or false, where is subgroup of...
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Exercise 14 Let G be a group. Which of the following statement(s) is/are true: I. If G is noncyclic, then there exists a proper non-cyclic subgroup of G. II. If a, b E G and Jal and |b| are finite, then Jab| is finite. III. NaEG C(a) = G if and only if G is abelian. (a) I and II only (b) II and III only () III only (d) II only (e) I and III only I don't see why (II) is false ??
Transcribed Image Text:Exercise 14 Let G be a group. Which of the following statement(s) is/are true: I. If G is noncyclic, then there exists a proper non-cyclic subgroup of G. II. If a, b E G and Jal and |b| are finite, then Jab| is finite. III. NaEG C(a) = G if and only if G is abelian. (a) I and II only (b) II and III only () III only (d) II only (e) I and III only I don't see why (II) is false ??
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