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Unformatted text preview: 9.4.3 ). By the induction hy-pothesis applied to K./ , j Aut K./ .L/ j D dim K./ L is nite. Therefore, Aut K .L/ is also nite, and j Aut K .L/ j D deg .p/ j Aut K./ .L/ j D dim K .K.// dim K./ .L/ D dim K L; where the rst equality comes from Equation ( 9.4.4 ), the second from the induction hypothesis and the irreducibility of p , and the nal equality from the multiplicativity of dimensions, Proposition 7.3.1 . n Corollary 9.4.17. Let K L be a nitedimensional Galois extension and M an intermediate eld. Then j Iso K .M;L/ j D dim K M: (9.4.5) Proof. j Iso K .M;L/ j D Aut K .L/ W Aut M .L/ D dim K .L/ dim M .L/ D dim K M;...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08