Two results for the automorphism group for partially commutative class two nilpotent groups. (Russian. English summary) Zbl 1249.20043
Summary: Let \(\Gamma\) be a finite simple graph, \(R\) be a binomial ring and \(G_\Gamma\) be a partially commutative \(R\)-group of nilpotency class 2 corresponding to the graph \(\Gamma\). In [V. N. Remeslennikov and A. V. Treier, Algebra Logic 49, No. 1, 43-67 (2010); translation from Algebra Logika 49, No. 1, 60-97 (2010; Zbl 1195.20039)] the study of \(\operatorname{Aut}(G_\Gamma)\) is reduced to the study of its unipotent part \(UT(G_\Gamma)\). Now we compute the nilpotency class and describe a generating set for \(UT(G_\Gamma)\). Moreover, we describe a generating set for \(\operatorname{Aut}(G_\Gamma)\).
MSC:
| 20F28 | Automorphism groups of groups |
| 20F18 | Nilpotent groups |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 20H20 | Other matrix groups over fields |
