(a) Show that the function f(x) = loger is an isomorphism from the group R+ of...

 

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(a) Show that the function f(x) = loger is an isomorphism from the group R+ of positive real numbers under multiplication onto the group R of real numbers under addition (b) Suppose that : Z20-> Z20 is an isomorphism with (9) = 7. Determine a formula for (2). = (c) Let G Z30 and H = <5> be the subgroup generated by 5. List all the elements of H and all the left cosets of H in G. (a) Show that the function f(x) = loger is an isomorphism from the group R+ of positive real numbers under multiplication onto the group R of real numbers under addition (b) Suppose that : Z20-> Z20 is an isomorphism with (9) = 7. Determine a formula for (2). = (c) Let G Z30 and H = <5> be the subgroup generated by 5. List all the elements of H and all the left cosets of H in G.