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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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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