3. Show that the correspondence theorem preserves indices. More precisely, ifa: G→ G'is a surjective group homomorphism, and ker a HCG and H' C G' are sub-groups that correspond under the correspondence theorem, then |G : H| = |G' : H'\.

Given that is a surjective group homomorphism.Let and are subgroups that correspond under the…

Answered: Show that the correspondence theorem…

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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Show that the correspondence theorem preserves indices. More precisely, if a: G→G' is a surjective group homomorphism, and ker a CH C G and H'G' are sub- groups that correspond under the correspondence theorem, then |G: H| = |G' : H'|.