Let G be a group of order 255. Show that G is not simple (hint: use a p-Sylow of G for some p).

Q: Prove that a group of order 28 must have an element of order 2.

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Q: Let G be a group. Suppose G=Z6xZ4. State all subgroups of G. Categorized(classify) the…

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Q: Let G = S4, the symmetric group of on 4 letters. H=A4 j) Show that the only two cosets of H are H…

A: elements of A4.All 3-cycles: {(123),(124),(132),(134),(142),(143),(234),(243)}.All permutations of…

Q: If G is a group of odd order and x ∈ G, show that x-1 is not in cl(x).

A: It is given that, G be a group of odd order and x∈G. Then, we have to show that x-1 is not in cl(x).…

Q: c. Define the maps 71 : G x H → G and 72 : G × H → H by 11(9, h) = g and 72(9, h) = h respectively.…

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Q: Write the Caley table of all non-abelian groups of order 8.

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Q: Show that a group of order 77 is cyclic.

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