Show that if H and K are subgroups of a group G, then their intersection H ∩ K is also a subgroup of G.

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A: Given: H and K are subgroups of G.We need to prove that H∩K is a subgroup of G and ∩i∈IHi is a…

Q: Chapter 2, exercise 10.2(a): Let H and K be subgroups of a group G. Prove that the intersection…

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Q: Let H and K be subgroups of a group G. Show that their intersection H ∩ K is also a subgroup of G.…

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Q: Let H be a proper subgroup of a finite group G. Show that G is notthe union of all conjugates of H.

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Q: let x and g be elements of a group G. show that x and gxg-1 have the same order. now prove that xy…

A: Hence, proved.Explanation:Step 1:To prove that x and gxg-1  have the same order for any elements x…

Q: Suppose H is a distant and normal subgroup of a group G. Prove that each subgroup of H is a normal…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: Let G = {a +b 2 ∈ ℝ │ a, b ∈ ℚ }. Prove that the nonzero elements of G form a group under…

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Q: any two elements x and y in a group G, there is a unique element z in G such that y = xz.

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Q: Let H and K be subgroups of the group G, and let a, b E G. Show that either aH n bK = Ø or else aH N…

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Q: Prove that the intersection of two subgroups is always a subgroup.

A: In this question, we prove the intersection of the two subgroup of G is also the subgroup of G.