From the explanations below, we have been able to show that if a Sylow P subgroup is normal then it is a characteristic subgroup.
First step here is to take finite group G with Sylow p-subgroup P. Thereafter, we prove that P ⊴ G ⟺ P is a characteristic subgroup of G.
If a Sylow subgroup is normal, then it is the unique subgroup of that same order. That means if P◃G, then there is only one subgroup of order |P| which tells us that P is characteristic since mapping the object to itself preserves orders of subgroups.
Question is;
Show that if a Sylow P subgroup is normal then it is characteristic subgroup.
Read more about Algebra Subgroups at; https://brainly.com/question/27794268
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