7. Let (G, *) and (K, o) be groups. Let ø: G → K be a group homomorphism (not neces- sarily an isomorphism). Prove that (a) $(eg) = eK, so O maps the identity of G into the identity of K. (b) Show that for all g E G, ø(g¬1) = [ø(g)]¬1. That is, o maps the inverse of g into the inverse of ø(g).

7. Let (G, *) and (K, o) be groups. Let ø: G → K be a group homomorphism (not neces- sarily an isomorphism). Prove that (a) $(eg) = eK, so O maps the identity of G into the identity of K. (b) Show that for all g E G, ø(g¬1) = [ø(g)]¬1. That is, o maps the inverse of g into the inverse of ø(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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