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(3) Let p be a prime number. Let G be the set of matrices of the form (7) 01 (x, y, z = Z/Zp). 0 1 Show that G is a group of order p³ which is not commutative. (b) Determine the class equation in the case p = 3. =

(3) Let p be a prime number. Let G be the set of matrices of the form (7) 01 (x, y, z = Z/Zp). 0 1 Show that G is a group of order p³ which is not commutative. (b) Determine the class equation in the case p = 3. =

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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Abstract Algebra

(3) Let be a prime number. Let G be the set of matrices of the form 1 x y (6:1) 01 (x, y, z = Z/Zp). 0 (a) Show that G is a group of order p³ which is not commutative. (b) Determine the class equation in the case p = = 3.
Transcribed Image Text:(3) Let be a prime number. Let G be the set of matrices of the form 1 x y (6:1) 01 (x, y, z = Z/Zp). 0 (a) Show that G is a group of order p³ which is not commutative. (b) Determine the class equation in the case p = = 3.
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