Recently there has been substantial progress towards computing the mod 2 cohomology of low rank sporadic simple groups. In fact the mod 2 cohomology of every sporadic simple group not containing (Z/2) has been computed, with the notable exceptions of HS (the Higman–Sims group) and Co3 (one of the Conway groups). The reason for these exceptions is that these two groups have large and complicated...

The guessing game introduced by Riis [Electron. J. Combin. 2007] is a variant of the “guessing your own hats” game and can be played on any simple directed graph G on n vertices. For each digraph G, it is proved that there exists a unique guessing number gn(G) associated to the guessing game played on G. When we consider the directed edge to be bidirected, in other words, the graph G is undirec...

Let Λ $\Lambda$ be a row-finite and source-free higher rank graph with finitely many vertices. In this paper, we define the Higman–Thompson-like group h t $\operatorname{\Lambda _{ht}}$ of C*-algebra O $\mathcal {O}_\Lambda$ to special subgroup unitary in . It is shown that closely related topological full groups groupoid associated Some properties are also investigated. We show its commutator ...