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Elements Of Modern Algebra

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 23E: 23. Prove that if and are normal subgroups of such that , then for all

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Prove that if H is a normal subgroup of G of prime index p then for all K < G either
(1) K < H or
(ii) G = HK and |K : K n H|= p.

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