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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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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