Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Inert subgroups and centralizers of involutions in locally finite simple groups
Download
index.pdf
Date
2003
Author
Özyurt, Erdal
Metadata
Show full item record
Item Usage Stats
187
views
0
downloads
Cite This
A subgroup H of a group G is called inert if [H : H \ Hg] is finite for all g 2 G. A group is called totally inert if every subgroup is inert. Among the basic properties of inert subgroups, we prove the following. Let M be a maximal subgroup of a locally finite group G. If M is inert and abelian, then G is soluble with derived length at most 3. In particular, the given properties impose a strong restriction on the derived length of G. We also prove that, if the centralizer of every involution is inert in an infinite locally finite simple group G, then every finite set of elements of G can not be contained in a finite simple group. In a special case, this generalizes a Theorem of Belyaev-Kuzucuoæglu-Seğckin, which proves that there exists no infinite locally finite totally inert simple group.
Subject Keywords
Involutes (Mathematics)
,
Finite simple groups
URI
http://etd.lib.metu.edu.tr/upload/1141546/index.pdf
https://hdl.handle.net/11511/13345
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Locally finite groups and their subgroups with small centralizers
ERSOY, KIVANÇ; Kuzucuoğlu, Mahmut; Shunwatsky, Pavel (2017-07-01)
Let p be a prime and G a locally finite group containing an elementary abelian p-subgroup A of rank at least 3 such that C-G(A) is Chernikov and C-G(a) involves no infinite simple groups for any a is an element of A(#). We show that G is almost locally soluble (Theorem 1.1). The key step in the proof is the following characterization of PSLp(k): An infinite simple locally finite group G admits an elementary abelian p-group of automorphisms A such that C-G(A) is Chernikov and C-G(A) Keywords: involves no inf...
NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS
Ercan, Gülin; Ogut, Elif (2014-01-01)
We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.
On abelian group actions with TNI-centralizers
Ercan, Gülin (2019-07-03)
A subgroup H of a group G is said to be a TNI-subgroup if for any Let A be an abelian group acting coprimely on the finite group G by automorphisms in such a way that for all is a solvable TNI-subgroup of G. We prove that G is a solvable group with Fitting length h(G) is at most . In particular whenever is nonnormal. Here, h(G) is the Fitting length of G and is the number of primes dividing A counted with multiplicities.
Torsion Generators Of The Twist Subgroup
Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2022-1-01)
We show that the twist subgroup of the mapping class group of a closed connected nonorientable surface of genus g >= 13 can be generated by two involutions and an element of order g or g -1 depending on whether 9 is odd or even respectively.
Centralizers of finite subgroups in Hall's universal group
Kegel, Otto H.; Kuzucuoğlu, Mahmut (2017-01-01)
The structure of the centralizers of elements and finite abelian subgroups in Hall's universal group is studied by B. Hartley by using the property of existential closed structure of Hall's universal group in the class of locally finite groups. The structure of the centralizers of arbitrary finite subgroups were an open question for a long time. Here by using basic group theory and the construction of P. Hall we give a complete description of the structure of centralizers of arbitrary finite subgroups in Ha...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
E. Özyurt, “Inert subgroups and centralizers of involutions in locally finite simple groups,” Ph.D. - Doctoral Program, Middle East Technical University, 2003.