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Recall the following groups: Z = {0, 1, 2, 3} (operation: addition mod 4) Z = {1,5, 7, 11} (operation: multiplication mod 12) Z = {1,3, 5 ,9, 11, 13} (operation: multiplication mod 14) %3D %3D %3D %3D (operation: matrix multiplication) Find the order of each element of Z, Z, Z, and GL(2, Z2).

Recall the following groups: Z = {0, 1, 2, 3} (operation: addition mod 4) Z = {1,5, 7, 11} (operation: multiplication mod 12) Z = {1,3, 5 ,9, 11, 13} (operation: multiplication mod 14) %3D %3D %3D %3D (operation: matrix multiplication) Find the order of each element of Z, Z, Z, and GL(2, Z2).

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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Recall the following groups: Z4 = {0, 1, 2, 3} (operation: addition mod 4) Z = {1,5, 7, 11} (operation: multiplication mod 12) Z = {1,3, 5, 9, 11, 13} (operation: multiplication mod 14) %3D %3! %3D (operation: matrix multiplication) Find the order of each element of Z4, Z, ZiA, and GL(2, Z2).
Transcribed Image Text:Recall the following groups: Z4 = {0, 1, 2, 3} (operation: addition mod 4) Z = {1,5, 7, 11} (operation: multiplication mod 12) Z = {1,3, 5, 9, 11, 13} (operation: multiplication mod 14) %3D %3! %3D (operation: matrix multiplication) Find the order of each element of Z4, Z, ZiA, and GL(2, Z2).
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