No description available.

One might easily argue that the Classification of Finite Simple Groups is one of the most important theorems of group theory. Given that any finite group can be deconstructed into its simple composition factors, it is of great importance to have a detailed knowledge of the structure of finite simple groups. One of the classes of finite groups that appear in the classification theorem are the simple classical groups, which are matrix groups preserving some form. This thesis will shed some new light on almost simple classical groups in dimension 13, 14 and 15. In particular we will determine their maximal subgroups. We will build on the results by Bray, Holt, and Roney-Dougal who calculated the maximal subgroups of all almost simple finite classical groups in dimension less than 12. Furthermore, Aschbacher proved that the maximal subgroups of almost simple classical groups lie in nine classes. The maximal subgroups in the first eight classes, i.e. the subgroups of geometric type, were determined by Kleidman and Liebeck for dimension greater than 13. Therefore this thesis concentrates on the ninth class of Aschbacher's Theorem. This class roughly consists of subgroups which are almost simple modulo scalars and do not preserve a geometric structure. As our final result we will give tables containing all maximal subgroups of almost simple classical groups in dimension 13, 14 and 15.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2018-03-14T17:24:36Z No. of bitstreams: 2 Dissertação - Angie Tatiana Suárez Romero - 2018.pdf: 2209912 bytes, checksum: 0ad7489cc1457ed892d896b3aa2f4885 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-03-15T11:07:28Z (GMT) No. of bitstreams: 2 Dissertação - Angie Tatiana Suárez Romero - 2018.pdf: 2209912 bytes, checksum: 0ad7489cc1457ed892d896b3aa2f4885 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-03-15T11:07:28Z (GMT). No. of bitstreams: 2 Dissertação - Angie Tatiana Suárez Romero - 2018.pdf: 2209912 bytes, checksum: 0ad7489cc1457ed892d896b3aa2f4885 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-03-05 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Cayley’s theorem allows us to represent a finite group as a permutations group of a finite set of points. In general, an action of a finite group G in a finite set, is described as an application of the group G in the symmetric group Sym(Ω). In this work we will describe some algorithms for permutation groups and implement them in the GAP system. We begin by describing a way of representing groups in computers, we calculate orbits, stabilizers in the basic form and by means of Schreier’s vectors. Later we make algorithms to work with primitive and transitive groups, thus arriving at the concept of BSGS, base and strong generator set, for permutation groups with the algorithm SCHREIERSIMS. In the end we work with group homomorphisms, we find the elements of a group through backtrack searches. / O Teorema de Cayley nos permite representar um grupo finito como grupo de permutações de um conjunto finito de pontos. De forma geral, uma ação de um grupo finito G em um conjunto finito Ω, é descrita como uma aplicação do grupo G no grupo simétrico Sym(Ω). Neste trabalho vamos descrever alguns algoritmos para grupos de permutação e implementa-los no sistema GAP. Começamos descrevendo uma maneira de representar grupos em computadores, calculamos órbitas, estabilizadores na forma básica e por meio de vetores de Schreier. Posteriormente fazemos algoritmos para trabalhar com grupos transitivos e primitivos, chegando assim ao conceito de, base e conjunto gerador forte (BSGS) para grupos de permutação finitos com o algoritmo SCHREIER-SIMS. No final trabalhamos com homomorfismos de grupos e encontramos os elementos de um grupo mediante pesquisas backtrack.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 97-98). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 97-98). Also available on the Internet.

Thesis--Princeton University. / Includes bibliographical references.

Thesis (Ph. D.)--University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 71-72). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

Thesis (M. Sc.)--Carleton University, 2002. / Includes bibliographical references (p. 37-38). Also available in electronic format on the Internet.

Thesis (M.A.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2009. / Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.