Dear readers, sorry for the lack of a proper post this week. I have been writing up my research into a paper, which I will upload here in full upon completion, and have been working on finding an upper bound on the number of leaves in Day, Sale and Wade's decomposition tree. Once I have this bound, I will make a post with the proof.
This blog post contains a summary of the results I obtained over the summer for this project. It is an overview that should be understandable to those without deep understanding of group theory. I am currently still working on a full paper that contains all the technical details required to be mathematically rigorous, which I intend to submit to various journals upon completion. Almost all the content of said paper can be found in the previous posts on this blog, though many of these contain mistakes which were later corrected, so such a reading might be difficult. The first draft of this paper has been completed, and once I have received feedback from experts in the field it will be completed. The deadline for research output for the URSS is at the end of October 2024, so whatever stage of completion this paper is at by that time I will upload to the Warwick URSS showcase website, and here on my blog.
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