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Consider the group G = SL(2,Z3) consisting of 2 x 2 matrices with entries in Z3 = {[0], [1], [2]} that have determinant equal to [1]. Find a 3-Sylow subgroup of G and write out its elements. Show that the subgroup generated by G) ([0] (1] and is a 2-Sylow subgroup of G.

Consider the group G = SL(2,Z3) consisting of 2 x 2 matrices with entries in Z3 = {[0], [1], [2]} that have determinant equal to [1]. Find a 3-Sylow subgroup of G and write out its elements. Show that the subgroup generated by G) ([0] (1] and is a 2-Sylow subgroup of G.

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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Consider the group G = SL(2,Z3) consisting of 2 x 2 matrices with entries in Z3 {[0], [1], [2]} that have determinant equal to [1]. Find a 3-Sylow subgroup of G and write out its elements. Show that the subgroup generated by [[0] [2] [1] [0] [1] [1]) and [1] [2] is a 2-Sylow subgroup of G.
Transcribed Image Text:Consider the group G = SL(2,Z3) consisting of 2 x 2 matrices with entries in Z3 {[0], [1], [2]} that have determinant equal to [1]. Find a 3-Sylow subgroup of G and write out its elements. Show that the subgroup generated by [[0] [2] [1] [0] [1] [1]) and [1] [2] is a 2-Sylow subgroup of G.
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