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Showing 1 to 20 of 79 for “"Finite Group"”.
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On moduli stacks of finite group schemes
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2000.
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Lifting Automorphisms to Stem Extensions of a Finite Group
A central extension of finite groups e: 0 (--->) A (--->) E (--->) G (--->)1 is said to be a stem extension of G if A is contained in the commutator subgroup E' of E. Schur showed that A must be isomorphic to a subgroup of the finite abelian group M = M(G) = H('2)(G,(//C)('(.))), where …
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Some irreducible complex representations of a finite group with BN pair
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1969.
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An Exploratory Study of the Abilities of Fifth and Seventh Grade Mathematics Students to Learn Finite Group Properties and Structures
Made available in DSpace on 2014-12-08T21:25:15Z (GMT). No. of bitstreams: 1 6910809.pdf: 7673251 bytes, checksum: 06805b3f6fd3b95070af32a246760974 (MD5) Previous issue date: 1968
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Fusion action systems by Matthew J.K. Gelvin.
… of fusion first arose in the local theory of finite groups. Puig abstracted the fusion data of a finite group to the notion of fusion system, an object that reflects local data in more abstract algebraic settings, such as the block theory of finite groups. Martino and Priddy conjectured that …
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Bounds on the Torsion Subgroups of Néron–Severi Groups
… identity component of Pic 𝑋. The Néron–Severi group scheme of 𝑋 is defined by NS 𝑋 = (Pic 𝑋)/(Pic⁰ 𝑋)ᵣₑ subscript d, and the Néron–Severi group of 𝑋 is defined by NS 𝑋 = (NS 𝑋)(𝑘). We give an explicit upper bound on the order of the finite group (NS 𝑋)ₜₒᵣ and the finite group scheme (NS 𝑋)ₜₒᵣ …
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Rationality of blocks of quasi-simple finite groups
… context of Donovan's conjecture for blocks of finite group algebras. Let P be a finite ℓ-group. Donovan's conjecture states that there are finitely many Morita equivalence classes of blocks of finite group algebras with defect groups isomorphic to P. Kessar proved that Donovan's conjecture …
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Fusion of Character Tables and Schur Rings of Dihedral Groups
A finite group H is said to fuse to a finite group G if the class algebra of G is isomorphic to an S-ring over H which is a subalgebra of the class algebra of H. We will also say that G fuses from H. In this case, the classes and characters of H can fuse to give the character table of G. We …
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Bounds on the genus of Riemann surfaces under certain group actions
The symmetric genus σ (G) of a finite group G is the smallest genus of those compact Riemann surfaces on which G acts faithfully, possibly reversing orientation. A natural question to ask is whether there exists a finite group G with σ (G) = g for any given non-negative integer g. It is known that …
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Tracial Rokhlin Property and Non-Commutative Dimensions
<p>This dissertation focuses on finite group actions with the tracial Rokhlin property and the structure of the corresponding crossed products. It consists of two major parts. For the first part, we study several different aspects of finite group actions with certain versions of the Rokhlin …
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On P-Radical P-Blocks of Group Algebras
p-Radical p-blocks of finite group algebras are studied. Much of the p-radical group theory is generalized to p-blocks through R. Knorr's work on simple induction and restriction pairs. In addition, several results concerning such blocks are proved.
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On tensor autoequivalences of graded fusion categories
… generalize the representation theory of finite groups. The simplest examples of fusion categories come from finite groups, their representations, and their cohomology. In general, it is useful to examine group theoretical features of fusion categories such as groups of (isomorphism …
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Verification of Dade's conjecture for Janko group J(,3)
… of a given defect d in a given p-block B of a finite group G in terms of the corresponding numbers $k(b, d)$ for blocks b of certain p-local subgroups of G.
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Ricci-flat deformations of orbifolds and asymptotically locally Euclidean manifolds
… a quotient of Euclidean space by the action of a finite group $\Gamma$. We adapt a slice construction by Ebin and the Calabi conjecture to orbifolds and show that for compact complex orbifolds with vanishing orbifold first Chern class and all infinitesimal complex deformations integrable, …
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The Irreducible Representations of D2n
<p>Irreducible representations of a finite group over a field are important because all representations of a group are direct sums of irreducible representations. Maschke tells us that if φ is a representation of the finite group G of order n on the m-dimensional space V over the field K of complex …
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Rational Schur Rings over Abelian Groups
… showed that the rational S-rings over a cyclic group Z_n are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Z_n. This idea is easily extended to show that for any finite group G, sublattices of the …
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Konstruktion rationaler Darstellungen endlicher Gruppen
… method to construct integral representaions of a finite group G. Starting point are the modular constituents of this representations for a prime p. An algorithm described in this work will construct an approximative representation over the p-adic integers. The construction of an integral …
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Commutativity Degree of Finite Groups
The commutativity degree of a group is the probability that two randomly selected (with replacement) elements of the group commute. We find bounds on the commutativity degree of a finite group, equate restricted values of commutativity degree to finite groups with particular structures, compute the …
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Composite Multi resolution Analysis Wavelets
… include additional dilations from a countable subgroup of the invertible matrices. We consider the case when these additional dilation matrices form a finite group. A theory of MRA wavelets is established in this setting along with a theory of shift invariant subspaces. We examine accuracy of this …
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Homology products on Z2-quotients of free loop spaces of spheres
… products on the homology of quotients by finite group actions of the free loop space ΛM of a compact manifold M. We compute some of the these products in the case M is as sphere. We show that there are nonnilpotent classes with respect to these products for spheres. The energy functional …
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