A problem in the Theory of Groups and a question related to FibonacciLike sequences

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Soggetto
Group theory; FibonacciAbstract
This thesis is composed of four chapters, two of which, Chapter 3 and Chapter 4, contain original results. In Chapter 1 we recall some basic notions and establish some of the notation and terminology which will be used in the sequel. For example, we recall some useful results about the class X of groups which are isomorphic to
their nonabelian subgroups. Every group of this class is in_nite and 2generated. This class of groups has been studied by H. Smith and J. Wiegold( [34]). They proved that every insoluble Xgroup is centre bysimple and they gave a complete characterization of soluble Xgroups. Then we recall some results about _nitely generated groups which are isomorphic to their nontrivial normal subgroups. In particular, we will use the result proved by J.C. Lennox, H. Smith and J. Wiegold in [17], for which if G is a _nitely generated in_nite group that is isomorphic to all its nontrivial normal subgroups and which contains a proper normal subgroup of _nite index, then G ' Z... [edited by author]
Descrizione
2013  2014
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Data
20160419Autore
Siani, Serena
Metadata
Mostra tutti i dati dell'itemAutori  Siani, Serena  
Data Realizzazione  20160808T09:02:36Z  
Date Disponibilità  20160808T09:02:36Z  
Data di Pubblicazione  20160419  
Identificatore (URI)  http://hdl.handle.net/10556/2180  
Descrizione  2013  2014  it_IT 
Abstract  This thesis is composed of four chapters, two of which, Chapter 3 and Chapter 4, contain original results. In Chapter 1 we recall some basic notions and establish some of the notation and terminology which will be used in the sequel. For example, we recall some useful results about the class X of groups which are isomorphic to their nonabelian subgroups. Every group of this class is in_nite and 2generated. This class of groups has been studied by H. Smith and J. Wiegold( [34]). They proved that every insoluble Xgroup is centre bysimple and they gave a complete characterization of soluble Xgroups. Then we recall some results about _nitely generated groups which are isomorphic to their nontrivial normal subgroups. In particular, we will use the result proved by J.C. Lennox, H. Smith and J. Wiegold in [17], for which if G is a _nitely generated in_nite group that is isomorphic to all its nontrivial normal subgroups and which contains a proper normal subgroup of _nite index, then G ' Z... [edited by author]  it_IT 
Lingua  en  it_IT 
Editore  Universita degli studi di Salerno  it_IT 
Soggetto  Group theory  it_IT 
Soggetto  Fibonacci  it_IT 
Titolo  A problem in the Theory of Groups and a question related to FibonacciLike sequences  it_IT 
Tipo  Doctoral Thesis  it_IT 
MIUR  MAT/02 ALGEBRA  it_IT 
Coordinatore  Longobardi, Patrizia  it_IT 
Ciclo  XIII n.s.  it_IT 
Tutor  Longobardi, Patrizia  it_IT 
CoTutor  Maj, Mercede  it_IT 
Dipartimento  Matematica  it_IT 