Let K be the splitting field of x3 – 5 over Q.• (a) Show that K = Q(5, iv3)• (b) Explicitly describe the elements of Aut(K)• (c) Determine what group we have seen before that Aut(K) isisomorphic to• (d) Draw a subgroup diagram for Aut(K) and subfield diagram ofK and indicate what subfields correspond to what subgroupsunder Galois correspondence.

Hi! For the part (c), we will be needing the information that what all groups we have seen before…

Answered: Let K be the splitting field of – 5…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 27E: 27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. ...

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Let K be the splitting field of – 5 over Q. - • (a) Show that K = Q(V5,i/3) • (b) Explicitly describe the elements of Aut(K)