I EXAMPLE 14 Inn(D,) To determine Inn(D,), we first observe that the complete list of inner auto- morphisms is R PR»» PRipo PRz Pµ• Þv• Þp• and øp.. Our job is to de- termine the repetitions in this list. Since R, R180*R1801 = x, so that Ro = PR, Also, &Rx) = R270XR270 RoR180*R180R90 = R90*R90 and D' = R,8 D, we have oH E Z(D,), we have dR x) = -1 = PR (x). Similarly, since H dy and o, = ¢p'. This proves that the R180 P 06, 180 previous list can be pared down to d Pre Pp reader to show that these are distinct (Exercise 15). and op. We leave it to the

I EXAMPLE 14 Inn(D,) To determine Inn(D,), we first observe that the complete list of inner auto- morphisms is R PR»» PRipo PRz Pµ• Þv• Þp• and øp.. Our job is to de- termine the repetitions in this list. Since R, R180R1801 = x, so that Ro = PR, Also, &Rx) = R270XR270 RoR180R180R90 = R90*R90 and D' = R,8 D, we have oH E Z(D,), we have dR x) = -1 = PR (x). Similarly, since H dy and o, = ¢p'. This proves that the R180 P 06, 180 previous list can be pared down to d Pre Pp reader to show that these are distinct (Exercise 15). and op. We leave it to the

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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