Algebra and Geometry | Part IA, 2006

Show that if HH and KK are subgroups of a group GG, then HKH \cap K is also a subgroup of GG. Show also that if HH and KK have orders pp and qq respectively, where pp and qq are coprime, then HKH \cap K contains only the identity element of GG. [You may use Lagrange's theorem provided it is clearly stated.]

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