Comparing Hobbes And Thrasymachus's View Of Justice

I think that Hobbes’s view of justice is not benefit individuals privately, whereas that of Thrasymachus states justice is the same thing everywhere, the advantage of the strongest (Plato 338b) which means that the ruler can do anything that he desires to do. He can make rules that will benefit him and that is private gains. Hobbes makes a clear definition that justice only exists under the state of Commonwealth, and there is no justice under the law of nature (LV Chapter 13.13, 15.3). The sovereign is the people, and it is established on the basis of keeping peace for its people, which means the limits of what justice is to Hobbes is different from Thraysymachus. It might be objected to this argument that both of them have the same idea. Nonetheless, Thrasymachus takes everything into accounts that the government will do anything that is beneficial to them. Hobbes’s sovereign, on the other hand, take things into consideration under the limits of security. As he says that justice is an obligation as long as it expands the purposes of all covenant which is self-preservation (LV chapter 15.7,8).
For Thrasymachus, the stronger group makes rules advantageous to themselves as he says that democracy makes democratic laws, tyranny makes tyrannical laws, and so on with others (Plato 338e). However, Hobbes thinks that justice or injustice can be inherited. For example, democracy is a form of just government, and tyranny must be unjust (LV Chapter 19.2). There might be some response against my point that both of their views are not really different. However, this argument fails because Hobbes makes a clear point that some types of governments can be unjust while Thrasymachus would say that all forms of government are just. Thus, by definition all kinds of government are just in Thrasymachus’s view but not for