Answer to Question #218674 in Abstract Algebra for Saifullah

Question

Let G be a nonabelian group of order 10 having golden ratio 1+√5 2 as the neutral element. Then:


(a) Verify class equation for G.


(b) Find all elements of Inn(G).


(c) Verify that G/Z(G) ∼ = Inn(G).


(d) For some elements x,y,z ∈ G: verify the commutator identity: [xy,z] = [x,z][x,z,y][y,z]