Let G be the group of all transformations on R which have the form x -→ ax + b where a, b e R, a ± 0. 1} is a normal subgroup of G. (i) Describe the right and left cosets of H to G. (ii) (iii) Is the subset K = {x → ax} a normal subgroup of G? Prove H = {x → ax + b | a =

Advanced Engineering Mathematics
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Let G be the group of all transformations on R which have the form x → ax + b
where a, b E R, a ± 0.
1} is a normal subgroup of G.
(i)
(ii)
(iii) Is the subset K = {x → ax} a normal subgroup of G?
(iv) Is G abelian? Is H abelian?
Prove H
{x → ax + b | a =
Describe the right and left cosets of H to G.
Transcribed Image Text:Let G be the group of all transformations on R which have the form x → ax + b where a, b E R, a ± 0. 1} is a normal subgroup of G. (i) (ii) (iii) Is the subset K = {x → ax} a normal subgroup of G? (iv) Is G abelian? Is H abelian? Prove H {x → ax + b | a = Describe the right and left cosets of H to G.
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