Let \( G \) be a group and let \( H \) and \( K \) be normal subgroups such that \( H \cap K = \{ e \} \). Let \[ \phi: G \rightarrow G/H \times G/K \] be the map \( \phi(g) = (Hg, Kg) \).Prove that the kernel of \( \phi \) is \(\{ e \} \).

Let be a group and let and be normal subgroups such that .Let be the map We have to…

Answered: Let G be a group and let H and K be…

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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Let G be a group and let H and K be normal subgroups such that HnK = {e}. Let : G→G/HxG/K be the map (g) = (Hg, Kg). Prove that the kernel of ois {e}.