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Let n ∈ N and let K be the intersection of all subgroups of G of order n. Prove that K is normal in G.

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 12E: Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...

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Let n ∈ N and let K be the intersection of all subgroups of G of order n. Prove that K is normal in G.

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