Questions of Abstract Algebra: 1. Find the order of the group of rigid motions of a cube. I3 . Give the lattice diagram of subgroups of Z,. 3. Are groups Z7,and Z3 isomorphic? Explain the reason. 4. Show that if G is a finite group with even number of elements, then there exists an element a G such that a # e and a = e. 5. Let G=14, X Z,,. Is this group cyclic? As you know any cyclic group can be generated by one element. If G is not cyclic, how many elements do you need to generate this group? What is the smallest size of a generating set? * 7 represents the set of integers