Let G = A4 and H = (1 2 3)). a) Find the left cosets of H in G. b) Find the right cosets of H in G. c) Is it true that for all g e G we have gH = Hg? d) Is it true that for all g e G there is some g' eG such that gH = Hg?

Let G = A4 and H = (1 2 3)). a) Find the left cosets of H in G. b) Find the right cosets of H in G. c) Is it true that for all g e G we have gH = Hg? d) Is it true that for all g e G there is some g' eG such that gH = Hg?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 36EQ

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Question

Let G = A4 and H = ((1 2 3)).
a) Find the left cosets of H in G.
b) Find the right cosets of H in G.
c) Is it true that for all g e G we have gH = Hg?
d) Is it true that for all g EG there is some g'e G such that gH = Hg?

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