The 2–dimension Series of the Just–nonsolvable Bsv Group

I compute the structure of the restricted 2–algebra associated to a group first described by Andrew Brunner, Said Sidki and Ana Cristina Vieira, acting on the binary rooted tree [4]. I show that its width is unbounded, growing logarithmically, and obeys a simple rule. As a consequence, the dimension of $n/$n+1 (where $ < 2Γ is the augmentation ideal), is p(0)+ · · ·+ p(n), the total number of partitions of numbers up to n. This paper contains many marginal notes. None, including this one, is necessary for the understanding of the results. However I hope that they will provide some insight into the motivation and process of discovery, as opposed to a description of the end result.