Let G be a group (not ncesssarily an Abelian group) of order 425. Prove that G must have an element of order 5.

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Q: Let G be a group (not necessarily an Abelian group) of order 425. Prove that G must have an element…

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Q: When can you say that a group is abelian.

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Q: The alternating group A5 has 5 conjugacy classes, of sizes 1, 12, 12, 15, 20. Use this information…

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Q: 2. Prove that a free group of rank > 1 has trivial center.

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Q: Write the Caley table of all abelian groups of order 8 Please be legible.

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Q: Q2 / If a, b and c are elements of a group (G,*) such that c*a=c*b then a=b.

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Q: 1. Let G = Z/36Z. (a) Find all subgroups of G, describe all containments between these subgroups,…

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Q: Let G be a group and suppose a, b ∈ G. Prove that (ab)^2 = a^2b^2 if and only if ab = ba.

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Q: Show that (4Z) (6Z) is a commutative group.

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