Probability of cyclicity of chains in finite groups. (English) Zbl 1538.20074
Summary: We introduce the probability of cyclicity of chains in finite groups and among other results we give explicit formulas for such probability of dihedral groups \(D_{2n}\), quasi-dihedral groups \(QD_{2n}\), generalized quaternion groups \(Q_{2n}\), and modular \(p\)-groups \(M_{p^n}\).
MSC:
20P05 | Probabilistic methods in group theory |
20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
20F05 | Generators, relations, and presentations of groups |
20D30 | Series and lattices of subgroups |