Let G be a group and let H be a normal subgroup of G. Prove that the factor group G/H is a group under the operation induced by the group operation of G. Hint: To prove that the factor group G/H is a group, you need to show that it satisfies the group axioms: closure, associativity, identity element, and inverse element. Remember to use the fact that H is a normal subgroup of G.

Let G be a group and let H be a normal subgroup of G. Prove that the factor group G/H is a group under the operation induced by the group operation of G. Hint: To prove that the factor group G/H is a group, you need to show that it satisfies the group axioms: closure, associativity, identity element, and inverse element. Remember to use the fact that H is a normal subgroup of G.

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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