(Given) Let G be a finite group and H1, H2, ..., Hk be subgroups of G. (Question) If H;< Hj, show that [G: H;] = [G : H;] [Hj : H;]. (Answer) We know that [G : H;] |G| |Hi| Given Hi< Hj →Hj N Hị = Hị Solution: =IG| |Hj n Hi| |Hi| [G: H;] |G| |G| |Hj] _ |G| |Hj| [G: H;] [Hj : H;] |Hj n Hi| |Hj| |Hj| |Hi|

(Given) Let G be a finite group and H1, H2, ..., Hk be subgroups of G. (Question) If H;< Hj, show that [G: H;] = [G : H;] [Hj : H;]. (Answer) We know that [G : H;] |G| |Hi| Given Hi< Hj →Hj N Hị = Hị Solution: =IG| |Hj n Hi| |Hi| [G: H;] |G| |G| |Hj] _ |G| |Hj| [G: H;] [Hj : H;] |Hj n Hi| |Hj| |Hj| |Hi|

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 4TFE: True or False Label each of the following statements as either true or false. Let H be a subgroup of...

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