5. Let p be a prime number and let Fp denote the field with p elements, Fp = {0, 1,..., p-1}, equipped with the operations of arithmetic modulo p. Consider the action of SL2 (Fp) on F2 defined by A(V) := Av. Show that the orbit of the vector (1) is the set of all nonzero vectors in F2. How many elements belong to the orbit and stabiliser of this vector? Use these answers to calculate |SL2(Fp)|.
5. Let p be a prime number and let Fp denote the field with p elements, Fp = {0, 1,..., p-1}, equipped with the operations of arithmetic modulo p. Consider the action of SL2 (Fp) on F2 defined by A(V) := Av. Show that the orbit of the vector (1) is the set of all nonzero vectors in F2. How many elements belong to the orbit and stabiliser of this vector? Use these answers to calculate |SL2(Fp)|.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...
Related questions
Question
![5. Let p be a prime number and let Fp denote the field with p elements,
Fp = {0, 1,...,p-1}, equipped with the operations of arithmetic modulo
p. Consider the action of SL2 (Fp) on F2 defined by TA(V) := Av. Show
that the orbit of the vector (1) is the set of all nonzero vectors in F2. How
many elements belong to the orbit and stabiliser of this vector? Use these
answers to calculate |SL2(Fp)|.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0de9773e-39c1-4df6-a7d6-864501c7f552%2F2828a116-bf02-420c-aea2-b510958194e6%2F8qx089h_processed.png&w=3840&q=75)
Transcribed Image Text:5. Let p be a prime number and let Fp denote the field with p elements,
Fp = {0, 1,...,p-1}, equipped with the operations of arithmetic modulo
p. Consider the action of SL2 (Fp) on F2 defined by TA(V) := Av. Show
that the orbit of the vector (1) is the set of all nonzero vectors in F2. How
many elements belong to the orbit and stabiliser of this vector? Use these
answers to calculate |SL2(Fp)|.
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