Please solve parts a,b, and d. Also please explain everything properly (ie. don't use part d for part a and b). Thanks. Exercise 7.21. (a) Prove that (2) is a maximal subgroup in Z (under addition).(b) Prove that (3) is a maximal subgroup in Z.(c) Show that (4) is not a maximal subgroup in Z.(d) Prove that (n) is a maximal subgroup of Z if and only if n is prime.

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Answered: ercise 7.21. (a) Prove that (2) is a…

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 20E

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ercise 7.21. (a) Prove that (2) is a maximal subgroup in Z (under addition). Prove that (3) is a maximal subgroup in Z. Show that (4) is not a maximal subgroup in Z. Prove that (n) is a maximal subgroup of Z if and only if n is prime.