(i) Write the Cauchy theorem (without proof).(ii) Prove that a - H, where H = {1,-1} is a group under multiplication.%3D

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(1) Write the Cauchy theorem (without proof).

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 18E: Let a and b be elements of a group G. Prove that G is abelian if and only if (ab)2=a2b2.

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(i) Write the Cauchy theorem (without proof).
(ii) Prove that a - H, where H = {1,-1} is a group under multiplication.
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