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statements. (a) If Ha = Hb, then b e Ha and a E Hb. %3D (b) If Ha = Hb, then aH = bH. (c) If aH = bH, then Ha-l = Hb-1. %3|

statements. (a) If Ha = Hb, then b e Ha and a E Hb. %3D (b) If Ha = Hb, then aH = bH. (c) If aH = bH, then Ha-l = Hb-1. %3|

Advanced Engineering Mathematics
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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Can you do all 2 problems ? (4 to 5) (You can only answer all the questions, you can't answer one question less) (If you don’t know one or more questions, please don’t answer, thank you)
4. Let H be a subgroup of a group G and a, b e G. Prove or disprove the following statements. (a) If Ha = Hb, then b e Ha and a E Hb. (b) If Ha = Hb, then aH = bH. (c) If aH = bH, then Ha-l = Hb-1. (d) If aH = bH, then a²H = 6²H. 5. Determine the class equation of A5.
Transcribed Image Text:4. Let H be a subgroup of a group G and a, b e G. Prove or disprove the following statements. (a) If Ha = Hb, then b e Ha and a E Hb. (b) If Ha = Hb, then aH = bH. (c) If aH = bH, then Ha-l = Hb-1. (d) If aH = bH, then a²H = 6²H. 5. Determine the class equation of A5.
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