Answered: Exercise 7.21. (a) Prove that (2) is a… | bartleby

Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 12E

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Please show steps and explain any theorems clearly. Also, please avoid using advanced theorems like Sylow's theorem, etc. 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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