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Articles 1 - 7 of 7
Full-Text Articles in Algebra
Representation Theory And Burnside's Theorem, Nathan Fronk
Representation Theory And Burnside's Theorem, Nathan Fronk
Senior Seminars and Capstones
In this paper we give a brief introduction to the representation theory of finite groups, and by extension character theory. These tools are extensions of group theory into linear algebra, that can then be applied back to group theory to prove propositions that are based entirely in group theory. We discuss the importance of simple groups and the Jordan-Hölder theorem in order to prepare for the statement of Burnside’s pq theorem. Lastly, we provide a proof of Burnside’s theorem that utilizes the character theory we covered earlier in the paper.
A Vector-Valued Trace Formula For Finite Groups, Miles Chasek
A Vector-Valued Trace Formula For Finite Groups, Miles Chasek
Electronic Theses and Dissertations
We derive a trace formula that can be used to study representations of a finite group G induced from arbitrary representations of a subgroup Γ. We restrict our attention to finite-dimensional representations over the field of complex numbers. We consider some applications and examples of our trace formula, including a proof of the well-known Frobenius reciprocity theorem.
Graded Character Rings, Mackey Functors And Tambara Functors, Beatrice Isabelle Chetard
Graded Character Rings, Mackey Functors And Tambara Functors, Beatrice Isabelle Chetard
Electronic Thesis and Dissertation Repository
Let $G$ be a finite group. The ring $R_\KK(G)$ of virtual characters of $G$ over the field $\KK$ is a $\lambda$-ring; as such, it is equipped with the so-called $\Gamma$-filtration, first defined by Grothendieck. In the first half of this thesis, we explore the properties of the associated graded ring $R^*_\KK(G)$, and present a set of tools to compute it through detailed examples. In particular, we use the functoriality of $R^*_\KK(-)$, and the topological properties of the $\Gamma$-filtration, to explicitly determine the graded character ring over the complex numbers of every group of order at most $8$, as well as …
On The Intersection Number Of Finite Groups, Humberto Bautista Serrano
On The Intersection Number Of Finite Groups, Humberto Bautista Serrano
Math Theses
Let G be a finite, nontrivial group. In a paper in 1994, Cohn defined the covering number of a finite group as the minimum number of nontrivial proper subgroups whose union is equal to the whole group. This concept has received considerable attention lately, mainly due to the importance of recent discoveries. In this thesis we study a dual concept to the covering number. We define the intersection number of a finite group as the minimum number of maximal subgroups whose intersection is equal to the Frattini subgroup. Similarly we define the inconjugate intersection number of a finite group as …
A Study Of Finite Symmetrical Groups, Patrick Kevin Martinez
A Study Of Finite Symmetrical Groups, Patrick Kevin Martinez
Theses Digitization Project
This study discovered several important groups that involve the classical and sporadic groups. These groups appeared as finite homomorphic images of the progenitors 3*8 : PGL₂(7), 2*¹⁴ : L₃ (2), 5*³ : S₃ and 7*2 : m S₃.
Construction Of Homomorphic Images, Stephanie Ann Hilber
Construction Of Homomorphic Images, Stephanie Ann Hilber
Theses Digitization Project
This thesis constructs several finite homomorphic images of infinite semi-direct products of the form 2*n:N.
Poincaré Duality, Christopher Michael Duran
Poincaré Duality, Christopher Michael Duran
Theses Digitization Project
This project is an expository study of the Poincaré duality theorem. Homology, cohomology groups of manifolds and other aglebraic and topological preliminaires are discussed.