Answered: Suppose 0: G-→ G be a homomorphism of…

Suppose 0: G-→ G be a homomorphism of groups. Show that: (i) Kere is normal in G (ii) The mappping o: G/ Ker0 →0(G) defined by þ(gKer0) = 0(g) is an isomorphism of groups.

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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B9. Show your step-by-step solution and answer.

Suppose 0: G→ G be a homomorphism of groups. Show that:
(i) Kere is normal in G
(ii) The mappping o: G/ Ker0 →0(G) defined by ø(gKer0) = 0(g) is an isomorphism of groups.

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