Answer all subpartsTrue or false and give proof. 1.Which of the following statements are true andwhich are false ? Give reasons for your answer :(a) The dihedralgroup D4 has five elements oforder two.In a group of odd order, the number ofconjugacy classes is also odd.(b)A free group on two generators has subfor 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 airreducible representation of degree 3 ordegree 4, but not both.(e)

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Description: Answer all subpartsTrue or false and give proof. 1.Which of the following statements are true andwhich are false ? Give reasons for your answer :(a) The dihedralgroup D4 has five elements oforder two.In a group of odd order, the number ofconjugacy cl

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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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...

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