Problem 2. Let (S3,0) be the group of rigid motions of an equilateral triangle. Denote by e = Ho, µ1 and µ2 the rotations by 0,120° and 240° counterclockwise respectively, and by o1,02 and o3 the axial symmetries. Find the partition of S3 = {µ0, H1, H2, 01,02,03} into a) left b) right cosets with respect to a subgroup H = {e,01}. 02

Problem 2. Let (S3,0) be the group of rigid motions of an equilateral triangle. Denote by e = Ho, µ1 and µ2 the rotations by 0,120° and 240° counterclockwise respectively, and by o1,02 and o3 the axial symmetries. Find the partition of S3 = {µ0, H1, H2, 01,02,03} into a) left b) right cosets with respect to a subgroup H = {e,01}. 02

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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