Sylow Theoremâ€™s is Group Theory are an important mathematical tool. Below we give a simple application of the theorems.
Theorem: If $$H$$ and $$K$$ are subgroups of $$G$$ and $$Hleq N_G(K)$$, then $$HK$$ is a subgroup of $$G$$. In particular, if $$K$$ is normal is $$G$$ then