Answered: Let H be a proper subgroup of a finite…

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Let H be a proper subgroup of a finite group G. Show that G is notthe union of all conjugates of H.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 10E: Let be a subgroup of a group with . Prove that if and only if .

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Question

Let H be a proper subgroup of a finite group G. Show that G is not
the union of all conjugates of H.

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