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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Centralizers Of Finite Subgroups In Simple Locally Finite Groups

Ersoy, Kivanc 01 August 2009 (has links) (PDF)
A group G is called locally finite if every finitely generated subgroup of G is finite. In this thesis we study the centralizers of subgroups in simple locally finite groups. Hartley proved that in a linear simple locally finite group, the fixed point of every semisimple automorphism contains infinitely many elements of distinct prime orders. In the first part of this thesis, centralizers of finite abelian subgroups of linear simple locally finite groups are studied and the following result is proved: If G is a linear simple locally finite group and A is a finite d-abelian subgroup consisting of semisimple elements of G, then C_G(A) has an infinite abelian subgroup isomorphic to the direct product of cyclic groups of order p_i for infinitely many distinct primes pi. Hartley asked the following question: Let G be a non-linear simple locally finite group and F be any subgroup of G. Is CG(F) necessarily infinite? In the second part of this thesis, the following problem is studied: Determine the nonlinear simple locally finite groups G and their finite subgroups F such that C_G(F) contains an infinite abelian subgroup which is isomorphic to the direct product of cyclic groups of order pi for infinitely many distinct primes p_i. We prove the following: Let G be a non-linear simple locally finite group with a split Kegel cover K and F be any finite subgroup consisting of K-semisimple elements of G. Then the centralizer C_G(F) contains an infinite abelian subgroup isomorphic to the direct product of cyclic groups of order p_i for infinitely many distinct primes p_i.
2

Enumeration of Factorizations in the Symmetric Group: From Centrality to Non-centrality

Sloss, Craig January 2011 (has links)
The character theory of the symmetric group is a powerful method of studying enu- merative questions about factorizations of permutations, which arise in areas including topology, geometry, and mathematical physics. This method relies on having an encoding of the enumerative problem in the centre Z(n) of the algebra C[S_n] spanned by the symmetric group S_n. This thesis develops methods to deal with permutation factorization problems which cannot be encoded in Z(n). The (p,q,n)-dipole problem, which arises in the study of connections between string theory and Yang-Mills theory, is the chief problem motivating this research. This thesis introduces a refinement of the (p,q,n)-dipole problem, namely, the (a,b,c,d)- dipole problem. A Join-Cut analysis of the (a,b,c,d)-dipole problem leads to two partial differential equations which determine the generating series for the problem. The first equation determines the series for (a,b,0,0)-dipoles, which is the initial condition for the second equation, which gives the series for (a,b,c,d)-dipoles. An analysis of these equa- tions leads to a process, recursive in genus, for solving the (a,b,c,d)-dipole problem for a surface of genus g. These solutions are expressed in terms of a natural family of functions which are well-understood as sums indexed by compositions of a binary string. The combinatorial analysis of the (a,b,0,0)-dipole problem reveals an unexpected fact about a special case of the (p,q,n)-dipole problem. When q=n−1, the problem may be encoded in the centralizer Z_1(n) of C[S_n] with respect to the subgroup S_{n−1}. The algebra Z_1(n) has many combinatorially important similarities to Z(n) which may be used to find an explicit expression for the genus polynomials for the (p,n−1,n)-dipole problem for all values of p and n, giving a solution to this case for all orientable surfaces. Moreover, the algebraic techniques developed to solve this problem provide an alge- braic approach to solving a class of non-central problems which includes problems such as the non-transitive star factorization problem and the problem of enumerating Z_1- decompositions of a full cycle, and raise intriguing questions about the combinatorial significance of centralizers with respect to subgroups other than S_{n−1}.
3

Enumeration of Factorizations in the Symmetric Group: From Centrality to Non-centrality

Sloss, Craig January 2011 (has links)
The character theory of the symmetric group is a powerful method of studying enu- merative questions about factorizations of permutations, which arise in areas including topology, geometry, and mathematical physics. This method relies on having an encoding of the enumerative problem in the centre Z(n) of the algebra C[S_n] spanned by the symmetric group S_n. This thesis develops methods to deal with permutation factorization problems which cannot be encoded in Z(n). The (p,q,n)-dipole problem, which arises in the study of connections between string theory and Yang-Mills theory, is the chief problem motivating this research. This thesis introduces a refinement of the (p,q,n)-dipole problem, namely, the (a,b,c,d)- dipole problem. A Join-Cut analysis of the (a,b,c,d)-dipole problem leads to two partial differential equations which determine the generating series for the problem. The first equation determines the series for (a,b,0,0)-dipoles, which is the initial condition for the second equation, which gives the series for (a,b,c,d)-dipoles. An analysis of these equa- tions leads to a process, recursive in genus, for solving the (a,b,c,d)-dipole problem for a surface of genus g. These solutions are expressed in terms of a natural family of functions which are well-understood as sums indexed by compositions of a binary string. The combinatorial analysis of the (a,b,0,0)-dipole problem reveals an unexpected fact about a special case of the (p,q,n)-dipole problem. When q=n−1, the problem may be encoded in the centralizer Z_1(n) of C[S_n] with respect to the subgroup S_{n−1}. The algebra Z_1(n) has many combinatorially important similarities to Z(n) which may be used to find an explicit expression for the genus polynomials for the (p,n−1,n)-dipole problem for all values of p and n, giving a solution to this case for all orientable surfaces. Moreover, the algebraic techniques developed to solve this problem provide an alge- braic approach to solving a class of non-central problems which includes problems such as the non-transitive star factorization problem and the problem of enumerating Z_1- decompositions of a full cycle, and raise intriguing questions about the combinatorial significance of centralizers with respect to subgroups other than S_{n−1}.
4

Extrapolação em espaços de Köthe / Extrapolation in Köthe spaces

Hernandez Del Toro, Victor Juan 29 January 2015 (has links)
Neste trabalho apresentamos alguns resultados da teoria de extrapolação desenvolvida pelo Nigel Kalton usando os conceitos de somas torcidas e espaço interpolado. / In this paper we present some results of extrapolation theory developed by Nigel Kalton using the concepts of twisted sums and interpolated space.
5

Sobre a influência dos centralizadores dos automorfismos de ordem dois em grupos de ordem ímpar / Centralizers of involutory automorphisms of groups of odd order

Rojas, Yerko Contreras 05 July 2013 (has links)
Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-09-18T15:33:16Z No. of bitstreams: 2 Dissertacao Yerko Contreras Rojas.pdf: 673331 bytes, checksum: 5359343f8c3a32e21369c3bc57917634 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-18T15:43:59Z (GMT) No. of bitstreams: 2 Dissertacao Yerko Contreras Rojas.pdf: 673331 bytes, checksum: 5359343f8c3a32e21369c3bc57917634 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-18T15:43:59Z (GMT). No. of bitstreams: 2 Dissertacao Yerko Contreras Rojas.pdf: 673331 bytes, checksum: 5359343f8c3a32e21369c3bc57917634 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-07-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This document presents an approach and development of some of the results of Shumyatsky in [14, 15, 16, 17, 18], where he worked with automorphisms of order two in finite groups of odd order, mainly showing the influence that the structure of the centralizer has on that of Group. Let G be a group with odd order, and ϕ an automorphism on G, of order two, where G = [G,ϕ], and given a limitation in the order of the centralizer of ϕ regard to G, CG(ϕ), which induces a limitation in the order of derived group G′ of group G, and we also verified that G has a normal subgroup H that is ϕ-invariant, such that H′ ≤ Gϕ and its index [G : H] is bounded with the initial limitation. With the same hypothesis of the group G and with the same limitation of the order of the centralizer of the automorphism, let V a abelian p-group such that G⟨ϕ⟩ act faithful and irreductible on V, then there is a bounded constant k, limitated by a function depending only on the parameter m, where m is tha limitation in the order of CG(ϕ), and elements x1, ...xk ∈ G−ϕ such that V = ρϕx 1,...,xk(V−ϕ). / O trabalho baseia-se na apresentação e desenvolvimento de alguns resultados expostos por Shumyatsky em [14, 15, 16, 17, 18], onde trabalha com automorfismos de ordem dois em grupos de ordem ímpar, mostrando fundamentalmente a influência da estrutura do centralizador do automorfismo na estrutura do grupo. Seja G um grupo de ordem ímpar e ϕ um automorfismo de G, de ordem dois, tal que G = [G,ϕ], dada uma limitação na ordem do centralizador de ϕ em G, CG(ϕ), a mesma induz uma limitação na ordem do grupo derivado G′ do grupo G, além disso verificamos que G tem um subgrupo H normal ϕ-invariante, tal que H′ ≤ Gϕ e o índice [G : H] é limitado dependendo da limitação inicial de CG(ϕ). Nas mesmas hipóteses do grupo G e com a mesma limitação da ordem do centralizador do automorfismo, seja V um p-grupo abeliano, tal que G⟨ϕ⟩ age fiel e irredutivelmente sobre V, então existe uma constante k, limitada por uma função que depende só da limitação de CG(ϕ), e elementos x1, ...xk ∈ G−ϕ, tal que V = ρϕx 1,...,xk(V−ϕ).
6

Extrapolação em espaços de Köthe / Extrapolation in Köthe spaces

Victor Juan Hernandez Del Toro 29 January 2015 (has links)
Neste trabalho apresentamos alguns resultados da teoria de extrapolação desenvolvida pelo Nigel Kalton usando os conceitos de somas torcidas e espaço interpolado. / In this paper we present some results of extrapolation theory developed by Nigel Kalton using the concepts of twisted sums and interpolated space.

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