Consider the group A5. (a) Compute a = (1,2, 3)(3, 4, 5) and ß = (1, 2, 3)(2, 3, 4). (b) List possible types of cyclic decompositions for elements in A5. (c) Show that for any distinct a, b, c E {1,2,3, 4, 5} there is y E A5 so that y(1,2, 3)y-1 = (a, b, c). (d) Deduce that if a normal subgroup N 4 A5 contains a 3-cycle (a, b, c), then N = A5. %3|

Consider the group A5. (a) Compute a = (1,2, 3)(3, 4, 5) and ß = (1, 2, 3)(2, 3, 4). (b) List possible types of cyclic decompositions for elements in A5. (c) Show that for any distinct a, b, c E {1,2,3, 4, 5} there is y E A5 so that y(1,2, 3)y-1 = (a, b, c). (d) Deduce that if a normal subgroup N 4 A5 contains a 3-cycle (a, b, c), then N = A5. %3|

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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