5. (a) Let σ = (1 2 3 4 5 6) in S6. Show that G...

(a) Let σ = (1 2 3 4 5 6) in S6. Show that G = {ε, σ, σ^2, σ^3, σ^4, σ^5} is a group using the operation of S6. Is G abelian? How many elements τ of G satisfy τ^2 = ε? τ^3 = ε? ε is the identity permutation.

(b) Show that (1 2) is not a product of 3-cycles. Must be written as a proof!

(d) Show that a group G is abelian if and only if (gh)^2 = (g^2)(h^2) for all g and h in G. Must be written as a proof!

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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