Since the popularisation of Rhetorical Analysis, it has been a commonplace to view 1:10 as the “thesis statement” or “propositio” of 1 Corinthians:
Now I appeal to you, brothers and sisters, by the name of our Lord Jesus Christ, that all of you should be in agreement and that there should be no divisions among you, but that you should be united in the same mind and the same purpose.
So, for example, this is the position of Margaret Mitchell and of Ben Witherington. According to their readings, this issue of “unity”/”division” is then the main theme of the letter, right through to its climax in chapter 15.
One reason I find this problematic is that chapter 15 just has to be squeezed so hard to make it fit: It simply isn’t presented as being about the problem or solution to ecclesial divisions. For this and other reasons, I like what I’ve recently encountered in a new German introduction to the New Testament: Pokorny and Heckel suggest that in fact, 1:18 ought to be viewed as the thesis statement of the letter:
For the message about the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God.
Pokorny and Heckel (p231) view it as no accident that the letter begins with an exploration of the cross and ends with an exploration of the resurrection. Amen to that!