Answered: Let f : G → H be a homomorphism with…

Let f : G → H be a homomorphism with kernel K. Show (a) K is a subgroup of G.(b) For any y ∈ H, f−1(y), the preimage of y, is a left coset of K.

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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Question

Let f : G → H be a homomorphism with kernel K. Show

(a) K is a subgroup of G.
(b) For any y ∈ H, f⁻¹(y), the preimage of y, is a left coset of K.

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