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1. Which of the following statements are true and which are false ? Give reasons for your answer: (a) The dihedral group D4 has five elements of order two. (b) In a group of odd order, the number of conjugacy classes is also odd.

1. Which of the following statements are true and which are false ? Give reasons for your answer: (a) The dihedral group D4 has five elements of order two. (b) In a group of odd order, the number of conjugacy classes is also odd.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Which of the following statements are true and which are false ? Give reasons for your answer : (a) The dihedral group D4 has five elements of order two. In a group of odd order, the number of conjugacy classes is also odd. (b) A free group on two generators has sub for every positive integer (c) groups of order n. n. (d) Z4 is the unique field with 4 elements. A finite group of order 12 can have a irreducible representation of degree 3 or degree 4, but not both. (e)
Transcribed Image Text:1. Which of the following statements are true and which are false ? Give reasons for your answer : (a) The dihedral group D4 has five elements of order two. In a group of odd order, the number of conjugacy classes is also odd. (b) A free group on two generators has sub for every positive integer (c) groups of order n. n. (d) Z4 is the unique field with 4 elements. A finite group of order 12 can have a irreducible representation of degree 3 or degree 4, but not both. (e)
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