The Posets of Classes of Isomorphic Subgroups of Finite Groups

The Posets of Classes of Isomorphic Subgroups of Finite Groups

In this paper we introduce and study the poset of equivalence classes of subgroups of a finite group G , induced by the isomorphism relation. This contains the well-known lattice of solitary subgroups of G . We prove that in several particular cases it determines the structure of G .

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Bulletin of the Malaysian Mathematical Sciences Society 2017, Vol.40 (1), p.163-172
1. Verfasser: Tărnăuceanu, Marius
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Isomorphism
Mathematics
Mathematics and Statistics
Set theory
Subgroups
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this paper we introduce and study the poset of equivalence classes of subgroups of a finite group G , induced by the isomorphism relation. This contains the well-known lattice of solitary subgroups of G . We prove that in several particular cases it determines the structure of G .
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-016-0319-1