OD-characterizability of the symmetric group \(\mathbb{S}_{27}\). (English) Zbl 1378.20039
Summary: Let \(G\) be a finite group with degree pattern \(D(G)\). A finite group \(G\) is called \(k\)-fold OD-characterizable if there are exactly \(k\) non-isomorphic groups \(H\) such that \(|G|=|H|\) and \(D(G)=D(H)\). In this paper our purpose is to correct an earlier paper [A. Mahmiani and the second author, Ital. J. Pure Appl. Math. 32, 7–14 (2014; Zbl 1333.20015)] and prove that the symmetric group on 27 letters is 38-OD-characterizable.
MSC:
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
| 20D06 | Simple groups: alternating groups and groups of Lie type |
| 20D05 | Finite simple groups and their classification |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
