Answered: Problem (1): Let r, s E Q with s t2 .r… | bartleby

Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 24E

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Problem (1): Let r, s € Q with s t² ·r for all t e Q and let E = Q[/r, Vs]. Prove that
Gal (E/Q) = Z/2Z × Z/2Z
and explicitly describe all four automorphisms and the fixed fields for every subgroup.

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