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A B D E All (iii) (i) (ii) None Which of the following are true? (i): H = {e, (1 2)} is a normal subgroup of S3. (ii): 6Z is a normal subgroup of 3Z. (iii): H= {e, (1 2)(3 4)} is a normal subgroup of An for any n 24.

A B D E All (iii) (i) (ii) None Which of the following are true? (i): H = {e, (1 2)} is a normal subgroup of S3. (ii): 6Z is a normal subgroup of 3Z. (iii): H= {e, (1 2)(3 4)} is a normal subgroup of An for any n 24.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question:** Which of the following are true? (i) \( H = \{ e, (1\ 2) \} \) is a normal subgroup of \( S_3 \). (ii) \( 6\mathbb{Z} \) is a normal subgroup of \( 3\mathbb{Z} \). (iii) \( H = \{ e, (1\ 2)(3\ 4) \} \) is a normal subgroup of \( A_n \) for any \( n \geq 4 \). **Options:** - A) All - B) (iii) - C) (i) - D) (ii) - E) None
Transcribed Image Text:**Question:** Which of the following are true? (i) \( H = \{ e, (1\ 2) \} \) is a normal subgroup of \( S_3 \). (ii) \( 6\mathbb{Z} \) is a normal subgroup of \( 3\mathbb{Z} \). (iii) \( H = \{ e, (1\ 2)(3\ 4) \} \) is a normal subgroup of \( A_n \) for any \( n \geq 4 \). **Options:** - A) All - B) (iii) - C) (i) - D) (ii) - E) None
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