(1) Let K be a finite extension of Q. Show that K contains onlyfinitely many roots of unity.

Let m = dim Q(K) and P∈K be a root of unity Then Q⊆QP⊆K Let n = o(P) ⇒ϕn=dimQ(QP)≤m

Answered: finite extension

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 31E: 31. Prove statement of Theorem : for all integers and .

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