Let G be a group. Show that for all a, b E G, (ab)2 = a2b2 G is abelian
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Q: (a) Show that a group G is abelian, if (ab)² = a²b², for a, b € G[C.
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Q: Prove the statement: Let g be a group, if g is abelian then (ab)2 = a2b2.
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A: A detailed solution is given below.
Q: 1. Show that the group (a, b, c|bª = a, c¬1 = b) is abelian. %3D
A: The objective is to show that the given group is abelian. Given group is: a,b,c|b4=a,c-1=b
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Q: Let G be a group. V a,b,c d and x in G, if axb=cxd then ab=cd then G is necessarily: O Abelian O Of…
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Q: Prove that a group G is Abelian if and only if (ab)-1 = a-1b-1 forall a and b in G.
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Q: OLet a and b be elements of a group G. Prove that G is abelian if and only if (ab)- = a¯\b-!.
A: Prove that G is abelian if and only if (ab)-1=a-1b-1. For all a and b be elements of a group G.
Q: Let G be a group and suppose that (ab)2 = a²b² for all a and b in G. Prove that G is an abelian…
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Q: Let G be a group. V a, b, c d and x in G, if axb = cxd then ab = cd then G is necessarily:…
A: The answer is given as follows :
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