Let X be a set, G a group, Sx={f:X→X | f is bijective on G} is a group with composition. Given x0∈X we consider all the elements of Sx that leave x0 fixed, that is, {f∈Sx | f(x0)=x0}. Show that this is a subgroup of Sx.

Let X be a set, G a group, Sx={f:X→X | f is bijective on G} is a group with composition. Given x0∈X we consider all the elements of Sx that leave x0 fixed, that is, {f∈Sx | f(x0)=x0}. Show that this is a subgroup of Sx.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 5E

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Let X be a set, G a group, S_x={f:X→X | f is bijective on G} is a group with composition. Given x₀∈X we consider all the elements of S_x that leave x₀ fixed, that is, {f∈S_x | f(x₀)=x₀}. Show that this is a subgroup of S_x.

Please be as clear as possible and legible, showing and explaining all the steps, and use definitions in necessary. Than you.

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