Assignment:
Q1) Prove there is no simple group of order 200.
Q2) Assume that a group G has two Sylow p-subgroups K and H. Prove that K and H are isomorphic.
Q3) Show that a group G of order 2p^n has proper normal subgroup, where p is odd prime number and n > 0.
Provide complete and step by step solution for the question and show calculations and use formulas.