5. Let G be a group and let H be a subgroup of G. For each g e G, we define the subset9H9¬1 of G bygHg{ghg¬l | h e H}.1Assume that |G| < o. Prove that-1H is normal in GgHgH for every g E G.(Hint for (): Show that for each g E G the mapPg : H → H, øg(h) = ghg¬1is well defined and bijective.)

G be a group and H is a subgroup of G. gH-1g is defined. We need to prove H is normal iff gH-1g=H…

5. Let G be a group and let H be a subgroup of G. For each g e G, we define the subset gHg-1 of G by 9H9¬ = {ghg¬ |he H}. -1 Assume that |G| < 00. Prove that H is normal in G A gHq-1 = H for every g E G. (Hint for () : Show that for each g E G the map g: H → H, 9(h) = ghg-1 is well defined and bijective.)

5. Let G be a group and let H be a subgroup of G. For each g e G, we define the subset gHg-1 of G by 9H9¬ = {ghg¬ |he H}. -1 Assume that |G| < 00. Prove that H is normal in G A gHq-1 = H for every g E G. (Hint for () : Show that for each g E G the map g: H → H, 9(h) = ghg-1 is well defined and bijective.)

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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