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 followingstatements.(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.

We shall answer first there suspects of 1st Que only. For others kindly post again by mentioning…

Answered: statements. (a) If Ha = Hb, then b e Ha…

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|

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 18E: 18. If is a subgroup of the group such that for all left cosets and of in, prove that is...

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Question

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.

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