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You searched for subject:(Normal Subgroups). Showing records 1 – 3 of 3 total matches.

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York University

1. Aliniaeifard, Farid. Normal Supercharacter Theories.

Degree: PhD, Mathematics & Statistics, 2018, York University

Classification of irreducible characters of some families of groups, for example, the family of the groups of unipotent upper-triangular matrices, is a "wild" problem. To have a tame and tractable theory for the groups of unipotent-upper triangular matrices Andr and Yan introduced the notion of supercharacter theory. Diaconis and Issacs axiomatized the concept of supercharacter theory for any group. In this thesis, for an arbitrary group G, by using sublattices of the lattice of normal subgroups containing the trivial subgroup and G, we build a family of integral supercharacter theories, called normal supercharacter theories (abbreviated NSCT). We present a recursive formula for supercharacters in an NSCT. The finest NSCT is constructed from the whole lattice of normal subgroups of G, and is a mechanism to study the behavior of conjugacy classes by the lattice of normal subgroups. We will uncover a relation between the finest NSCT, faithful irreducible characters, and primitive central idempotents. We argue that NSCT cannot be obtained by previous known supercharacter theory constructions, but it is related to *-products of some certain supercharacter theories. We also construct an NSCT for the family of groups of unipotent upper-triangular matrices. These groups are crucial to the supercharacter theory. The supercharacters of the resulting NSCT are indexed by Dyck paths, which are combinatorial objects that are central to several areas of algebraic combinatorics. Finally, we show that this supercharacter construction is identical to Scott Andrews' construction after gluing the superclasses and the supercharacters by the action of the torus group. Advisors/Committee Members: Bergeron, Nantel (advisor).

Subjects/Keywords: Mathematics; Character Theory; Supercharacter Theory; Lattice Theory; Normal Subgroups; Group Theory; Lattice of Normal Subgroups; Primitive Central Idempotents

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APA (6th Edition):

Aliniaeifard, F. (2018). Normal Supercharacter Theories. (Doctoral Dissertation). York University. Retrieved from http://hdl.handle.net/10315/34307

Chicago Manual of Style (16th Edition):

Aliniaeifard, Farid. “Normal Supercharacter Theories.” 2018. Doctoral Dissertation, York University. Accessed November 26, 2020. http://hdl.handle.net/10315/34307.

MLA Handbook (7th Edition):

Aliniaeifard, Farid. “Normal Supercharacter Theories.” 2018. Web. 26 Nov 2020.

Vancouver:

Aliniaeifard F. Normal Supercharacter Theories. [Internet] [Doctoral dissertation]. York University; 2018. [cited 2020 Nov 26]. Available from: http://hdl.handle.net/10315/34307.

Council of Science Editors:

Aliniaeifard F. Normal Supercharacter Theories. [Doctoral Dissertation]. York University; 2018. Available from: http://hdl.handle.net/10315/34307


Brigham Young University

2. Clemens, Miles A. Normally Supportive Sublattices of Crystallographic Space Groups.

Degree: MS, 2018, Brigham Young University

Normal subgroups can be thought of as the primary building blocks for decomposing mathematicalgroups into quotient groups. The properties of the resulting quotient groups are oftenused to determine properties of the group itself. This thesis considers normal subgroups of threedimensionalcrystallographic space groups that are themselves three-dimensional crystallographicspace groups; for convenience, we refer to such a subgroup as a csg-normal subgroup. We identifypractical restrictions on csg-normal subgroups that facilitate their tabulation. First, the point groupof an csg-normal subgroup must be a normal subgroup of the crystallographic point group of thespace group, which we refer to for convenience as a cpg-normal subgroup. For each of the cpgnormalsubgroups, which are all well known, we identify the abstract quotient group. Secondly,we identify necessary conditions on the sublattice basis of any csg-normal subgroup, and tabulatethe “normally supportive“ sublattices that meet these conditions, where some tables are symbolicforms that represent infinite families of sublattices. For a given space group, every csg-normalsubgroup must be an extension of such a normally supportive sublattice, though some normallysupportive sublattices may not actually support such extensions.

Subjects/Keywords: space groups; normal subgroups; crystallography; Physical Sciences and Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Clemens, M. A. (2018). Normally Supportive Sublattices of Crystallographic Space Groups. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=8705&context=etd

Chicago Manual of Style (16th Edition):

Clemens, Miles A. “Normally Supportive Sublattices of Crystallographic Space Groups.” 2018. Masters Thesis, Brigham Young University. Accessed November 26, 2020. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=8705&context=etd.

MLA Handbook (7th Edition):

Clemens, Miles A. “Normally Supportive Sublattices of Crystallographic Space Groups.” 2018. Web. 26 Nov 2020.

Vancouver:

Clemens MA. Normally Supportive Sublattices of Crystallographic Space Groups. [Internet] [Masters thesis]. Brigham Young University; 2018. [cited 2020 Nov 26]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=8705&context=etd.

Council of Science Editors:

Clemens MA. Normally Supportive Sublattices of Crystallographic Space Groups. [Masters Thesis]. Brigham Young University; 2018. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=8705&context=etd

3. Melchor Borja, Carmen. Conjugacy classes and normal subgroups in finite groups.

Degree: Departament de Matemàtiques, 2018, Universitat Jaume I

Esta tesis se enmarca dentro del estudio que analiza la influencia de las clases de conjugación en la estructura de grupos finitos. En las últimas décadas ésta ha sido una línea de investigación próspera y activa. Los contenidos están divididos en dos partes. La primera consta de cuatro capítulos sobre grafos de clases de conjugación contenidas en un subgrupo normal y su impacto estructural en este subgrupo. Además, como aplicación de las propiedades de estos grafos, presentamos una versión generalizada del conocido Teorema de Landau para este tipo de clases. La segunda parte contiene dos capítulos que tratan sobre la información que el producto de clases de conjugación proporciona acerca de la no simplicidad del grupo y la estructura normal y resolubilidad de algunos subgrupos asociados a estas clases. Advisors/Committee Members: [email protected] (authoremail), false (authoremailshow), Beltrán Felip, Antonio (director), Felipe Román, María José (director).

Subjects/Keywords: Finite groups; Normal subgroups; Conjugacy classes; Graphs; Product of classes; Ciències naturals, químiques, físiques i matemàtiques; 51

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Melchor Borja, C. (2018). Conjugacy classes and normal subgroups in finite groups. (Thesis). Universitat Jaume I. Retrieved from http://hdl.handle.net/10803/664896

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Melchor Borja, Carmen. “Conjugacy classes and normal subgroups in finite groups.” 2018. Thesis, Universitat Jaume I. Accessed November 26, 2020. http://hdl.handle.net/10803/664896.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Melchor Borja, Carmen. “Conjugacy classes and normal subgroups in finite groups.” 2018. Web. 26 Nov 2020.

Vancouver:

Melchor Borja C. Conjugacy classes and normal subgroups in finite groups. [Internet] [Thesis]. Universitat Jaume I; 2018. [cited 2020 Nov 26]. Available from: http://hdl.handle.net/10803/664896.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Melchor Borja C. Conjugacy classes and normal subgroups in finite groups. [Thesis]. Universitat Jaume I; 2018. Available from: http://hdl.handle.net/10803/664896

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.