Plato's Republic Book I: Is “Justice” nothing but the Rule of the Strong?

If there were only one book other than the Bible with which to educate yourself, then this would probably be a good choice. For the next 10 meetups, we shall be reading one book of Plato's "Republic" at a time.
In previous meetups we have read and discussed the trial and death of Socrates, during which Socrates has explained that there is a part of the human called "the soul" harmed by being unjust and benefitted by being just, and that this part of man is his "true self". In this longer ten part work Plato dives deeper into this claim and attacks/defends it from many angles. In this first chapter, Socrates' main opponent is the sophist Thrasymachus who claims that "justice is the rule of the stronger". Most readers will think that this view is that of Nietzsche, some will also see that this is also very close to Marx's view. Although it seems that Socrates has apparently defeated Thrasymachus, in my view Plato knows that this view can be adjusted to avoid the rebuttals given by Socrates.
Another possible quest is to look for signs of Plato’s doubts about whether he has really defeated Thrasymachus aand hints about what his own hidden view might be. Some people might think that he's trying to hide the weakness of his own view. If this were true, then writing an entire book focussing on the weaknesses of his view is probably not the way to go. I think he's got a reason for everything he says… and doesn't say. We often have things that we believe for good reasons and yet also have good reasons for not openly revealing them. I think it's likely that Plato is trying to reveal to some and conceal his real views from others. This view is not original to me but common to many authors, and I feel like in the next year I would like to research this.