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f H and K are two subgroups of a group G, then show that for any a, b ∈ G, either Ha ∩ Kb = ∅ or Ha ∩ Kb = (H ∩ K)c for some c ∈ G.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 18E: 18. If is a subgroup of the group such that for all left cosets and of in, prove that is...

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Question

If H and K are two subgroups of a group G, then show that for any a, b ∈ G,
either Ha ∩ Kb = ∅ or Ha ∩ Kb = (H ∩ K)c for some c ∈ G.

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