QI/AI Prove that the mathematical system (s), where (o) is an usual composition map is a group? B/ Write the element of the group S, and prove that it is not abelian group?

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

A: We have to write cayley table of abelian group of order 8.

Q: Write under isomorphism all the abelian groups of order 8 and their respective subgroups.

A: To find all the abelian groups of order 8, we can use the fundamental theorem of finitely generated…

Q: If ?^2 = ? for each element “a” of a group G, where “e” is the identity, then prove that G is…

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Q: Let G = : a – b = c – d, a,b, c, d E R Show that G is a group under (the usual) matrix addition.

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

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Q: Let a and b be elements in a group G. Prove that ab^(n)a^(−1) = (aba^(−1))^n for n ∈ Z.

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Q: not

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