Solution for problem 19.33 Chapter 19
Prove that if p is a prime, then Aut(Zp) "" Zp_l
Modern Algebra: An Introduction | 6th Edition
Problem 19.33
Prove that if p is a prime, then Aut(Zp) "" Zp_l.
Accepted Solution
Step-by-Step Solution:
Step 1 of 3
Non Homogeneous Linear nth Order DE. Solutions to ▯ n n▯1 2 ▯ (n) (n▯1) 00 0 Ly = a n + a n▯1D + ▯▯▯ + a2D + a D1+ a 0 y = any + an▯1 y + ▯▯▯ + a2y + a 1 + a y0= F(x); (1) where F(x) 6= 0: Every solution of this nonhomogeneous equation is of the form yG(x) = y cx) + y px) (2) where y (x) is the general solution to the homogeneous counterpart of the DE c ▯ ▯ Ly = a D + a D n▯1 + ▯▯▯ + a D + a D + a y = a y(n)+ a y (n▯1)+ ▯▯▯ + a y + a y + a y = 0; (3)
Chapter 19, Problem 19.33 is Solved
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Prove that if p is a prime, then Aut(Zp) "" Zp_l