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Recall from question 2 of the last assignment the subgroup 1 ab S = 0 1 1 c: a, b, Ce Zs SL3(Zs). 0 0 1 As a matrix group S can act on the vector space Z. Find all the orbits of this action and for each orbit determine the stabilizer of one of the points.

Recall from question 2 of the last assignment the subgroup 1 ab S = 0 1 1 c: a, b, Ce Zs SL3(Zs). 0 0 1 As a matrix group S can act on the vector space Z. Find all the orbits of this action and for each orbit determine the stabilizer of one of the points.

Advanced Engineering Mathematics
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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Solve q1 and use the information from second picture that i highlight by red pen Plz solve this correctly i need perfect soloution
2. Consider the subset 1 S = 0 1 c : a, b, c E Z, > C SL3(Z3). 0 0 1 (a) Show that S is a subgroup of SL3(Z3). (b) Show that every non-trivial element of S has order 3. (c) Is S abelian? Justify your answer.
Transcribed Image Text:2. Consider the subset 1 S = 0 1 c : a, b, c E Z, > C SL3(Z3). 0 0 1 (a) Show that S is a subgroup of SL3(Z3). (b) Show that every non-trivial element of S has order 3. (c) Is S abelian? Justify your answer.
1. Recall from question 2 of the last assignment the subgroup -{() 1 a b 0 1 c 0 0 1 S = b, ce Z< SL3(Zs). As a matrix group S can act on the vector space Z. Find all the orbits of this action and for each orbit determine the stabilizer of one of the points.
Transcribed Image Text:1. Recall from question 2 of the last assignment the subgroup -{() 1 a b 0 1 c 0 0 1 S = b, ce Z< SL3(Zs). As a matrix group S can act on the vector space Z. Find all the orbits of this action and for each orbit determine the stabilizer of one of the points.
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