group of order 126 cannot be simple
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Prove that a group of order 126 cannot be simple
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- Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.Let be a group of order , where and are distinct prime integers. If has only one subgroup of order and only one subgroup of order , prove that is cyclic.9. Find all homomorphic images of the octic group.
- Prove that if r and s are relatively prime positive integers, then any cyclic group of order rs is the direct sum of a cyclic group of order r and a cyclic group of order s.Find all homomorphic images of the quaternion group.Suppose that G is a finite group. Prove that each element of G appears in the multiplication table for G exactly once in each row and exactly once in each column.