Let K be a finite field of order q = p", with p an odd prime number and n 2 1.We denote by K×² the set of squares in K*a) Prove that K×2 is a subgroup of K* of order ,1.

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Answered: Let K be a finite field of order q =…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 22E: 22. Let be a ring with finite number of elements. Show that the characteristic of divides .

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Let K be a finite field of order q = p", with p an odd prime number and n > 1. We denote by K×² the set of squares in K* a) Prove that K×2 is a subgroup of K* of order 1.