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14. Prove that each of the following maps is a group homomorphism. ) The map : Z → Z/NZ that sends a € Z to a mod N in Z/NZ. a -) The map : R* → GL2 (R) defined by (a) = (-1). a :) The discrete logarithm map log, : F→ Z/(p-1)Z, where g is a primitive root modulo p.

14. Prove that each of the following maps is a group homomorphism. ) The map : Z → Z/NZ that sends a € Z to a mod N in Z/NZ. a -) The map : R* → GL2 (R) defined by (a) = (-1). a :) The discrete logarithm map log, : F→ Z/(p-1)Z, where g is a primitive root modulo p.

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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2.14. Prove that each of the following maps is a group homomorphism. (a) The map : Z → Z/NZ that sends a € Z to a mod N in Z/NZ. a 0 (b) The map : R* → GL2(R) defined by ø(a) = (%º₁). (c) The discrete logarithm map logg: F→ Z/(p-1)Z, where g is a primitive root modulo p.
Transcribed Image Text:2.14. Prove that each of the following maps is a group homomorphism. (a) The map : Z → Z/NZ that sends a € Z to a mod N in Z/NZ. a 0 (b) The map : R* → GL2(R) defined by ø(a) = (%º₁). (c) The discrete logarithm map logg: F→ Z/(p-1)Z, where g is a primitive root modulo p.
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