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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 25E

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Answer these question with ONLY BRIEF EXPLANATION

Suppose U(50) is generated by 3. Find |31|.
Which of the following is a generator of Z72?
А. 39
В. 51
С. 45
D. 65
Find the number of elements in the cyclic group of Z14 generated by 6.

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Exercises 9. For each of the following values of, find all distinct generators of the cyclic group under addition. a. b. c. d. e. f.
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For each of the following values of n, find all distinct generators of the group Un described in Exercise 11. a. n=7 b. n=5 c. n=11 d. n=13 e. n=17 f. n=19
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Answer 20 and 21
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Pls answer 1 to 3
Indicate the eight elements of the group 4 14 = = {z E C such that z₁ = 1}, the 4th root of unity on the circle (C1-2)shown below. Also list the elements of the group.
Q 5 Find the inverse of the element 9 in the group (U(10), ®10). Q 6 Find the order of the element 2 in the group (Zs, s). Q 7 Find the generators of the group (Z9, ®9). Q 8 List all the subgroups of the group (Z4, ®4).
Answer 16 and 17

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