Return to search

Sobre grupos radicales localmente finitos con min-p para todo primo p.

SUMARYA group is said to be locally finite if every finite subset of G generates a fi-nite subgroup. The class of locally finite groups is placednear the cross-roads of finite group theory and the general theory of infinite groups. Many theoremsabout finite groups can be phrased in such a way that their statements still make sense for locally finite groups. However, in general, Sylow's Theorems do not hold in the class of locally finite groups and there are a numberof generic examples which show that locally finite groups can be very varied and complex. If we restrict our attention to locally finite-soluble groups with min-p for all primes p then the Sylow ¼-subgroups are very well behavedif ¼ or its complementary in the set of all primes is finite. The conjugacy of Sylow p-subgroups in these groups is a very strong condition which have guaranteed the successful development of formation theory and interestingresults on Fitting classes in the universe c¯L of all radical locally finite groups with min-p for all primes p. Moreover, using an extension of the Frattini subgroup introduced by Tomkinson, it has been proved a Gasch¨utz-Lubeseder type theorem characterizing saturated formations in this universe.It is therefore appropriate to study the class c¯L of all radical locally finitegroups with min-p for all primes p in more detail. In this thesis we haveobtained results which help to understand better the groups in this class.Consequently, the unspoken rule is that all groups considered in the threechapters of this thesis belong to the class c¯L. The work is organized as follows.In Chapter 1, we explore the class B of generalized nilpotent groups inthe universe c¯L. We obtain that this class behaves in the universe c¯L as thenilpotent groups in the finite universe and we determine the structure of B-groups explicitly. Moreover, we show that the largest normal B-subgroup ofa c¯L-group is the Fitting subgroup. This fact allows us to prove some results1concerning the Fitting subgroup of a c¯L-group which are extensions of thefinite ones. The aim of the last section is to study the injectors associatedto the class B. In fact, we obtain a description of the B-injectors similar tothe characterization of nilpotent injectors of a finite soluble group.Chapter 2 is devoted to study the local version of the class B. This isa natural generalization of the class of finite p-nilpotent groups. We extendsome results of finite groups to the above universe using a local version ofa Frattini-like subgroup. In particular, some properties appear relating theFrattini and Fitting subgroups. The injectors associated to this class ofgeneralized p-nilpotent groups are also characterized.Finally, Chapter 3 is concerned with the structure of a radical locallyfinite group with min-p for all p, G = AB, factorized by two subgroups Aand B in the class B. We extend the well-known results of finite productsof nilpotent groups to the above universe.We have introduced a Chapter 0 establishing the notation and terminology.It also presents many of the well-known results that will be usedthroughout this thesis.

Identiferoai:union.ndltd.org:TDX_UV/oai:www.tdx.cat:10803/9462
Date27 March 2003
CreatorsPedraza Aguilera, Tatiana
ContributorsBallester Bolinches, Adolfo, Universitat de València. Departament d'Àlgebra
PublisherUniversitat de València
Source SetsUniversitat de València
LanguageSpanish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/doctoralThesis, info:eu-repo/semantics/publishedVersion
Formatapplication/pdf
SourceTDX (Tesis Doctorals en Xarxa)
RightsADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel·lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant als continguts de la tesi com als seus resums i índexs., info:eu-repo/semantics/openAccess

Page generated in 0.0024 seconds