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. Please be as clear as possible and use definitions in necessary. Than you a lot.

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. Please be as clear as possible and use definitions in necessary. Than you a lot.

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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