A Note on Solitary Subgroups of Finite Groups |
| |
Authors: | R Esteban-Romero Orieta Liriano |
| |
Institution: | 1. Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, València, SpainRamon.Esteban@uv.es resteban@mat.upv.es;3. Departamento de Matemática, Universidad Autónoma de Santo Domingo and Ciclo General, área de Matemática, Universidad Iberoamericana, Santo Domingo, Dominican Republic |
| |
Abstract: | We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N. We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups. |
| |
Keywords: | Finite group Fitting class Formation Quotient solitary subgroup Solitary subgroup |
|
|