Abstract Algebra Questions... Help Please!! Any and all help on these problems would be greatly appreciated. Thank you in advance to any who offer help . 1. Let φ:G->H be a group homomorphism, where G has order p, a prime number. show that φ is either one-to-one or maps every element of G to the identity element of H. 2. Show that if H is a normal subgroup of G (with operation multiplication) and [G]=m, then for every g in G, g^m is in H. 3. Every symmetry of the cube induces a permutation of the four diagonals connecting the opposite vertices of the cube. This yields a group homomorphism φ from the group G of symmetris of the Cube to S4 (4 is a subscript). Does φ map G onto S4? Is φ 1-1? If not, describe the symmetries in the kernel of φ. Determine the order of G.