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Showing 1 to 12 of 12 for “"Sylow"”.
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The Green Correspondences for Finite-Groups With a Cyclic Sylow Subgroup
Made available in DSpace on 2014-12-11T18:24:10Z (GMT). No. of bitstreams: 1 7414638.pdf: 1636170 bytes, checksum: 8131f134e72364f25f72bb132f9d346d (MD5) Previous issue date: 1974
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Relative Springer isomorphisms and the conjugacy classes in Sylow p-subgroups of Chevalley groups
… are \(F\)-stable and that \(U(q)\) is a Sylow \(p\)-subgroup of \(G(q)\). We study the adjoint orbits of \(U\) and show that the conjugacy classes of \(U(q)\) are in correspondence with the \(F\)-stable adjoint orbits of \(U\). This allows us to deduce results about the conjugacy classes …
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The Structure of the 2-Sylow Subgroups of the Ideal Class Groups of Imaginary Bicyclic Biquadratic Fields
In this dissertation class groups of imaginary bicyclic biquadratic fields are considered. In chapter 1 we develop a method for determining the structure of the 2-class group of K. In chapters 3, 4, and 5 this method is applied to determine all imaginary bicyclic biquadratic extensions of Q with …
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Saturated fusion systems and finite groups
… of saturated fusion systems over a Sylow p-subgroup of SL\(_3\)(q) (which has shape q\(^3\) : q). This extends a result of Albert Ruiz and Antonio Viruel, who studied the case when q = p in [36]. As an immediate consequence of this result we shall have a complete classification of …
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The Macdonald group
… for α ̸= 1, G(α) is the direct product of its Sylow subgroups. In the first third of the thesis, we determine the order, upper and lower central series, nilpotency class, and exponent of each of these Sylow subgroups. For the remaining two thirds of the thesis we concentrate on the Sylow …
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On the Units and the Structure of the 3-Sylow Subgroups of the Ideal Class Groups of Pure Bicubic Fields and their Normal Closures
If we adjoin the cube root of a cube free rational integer <i>m</i> to the rational numbers we construct a cubic field. If we adjoin the cube roots of distinct cube free rational integers <i>m</i> and <i>n</i> to the rational numbers we construct a bicubic field. The number theoretic invariants for …
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On Problems in the Representation Theory of Symmetric Groups
… of the symmetric groups $\mathfrak{S}_n$, their Sylow $p$-subgroups $P_n$ and related algebras. For all primes $p$ and natural numbers $n$, we determine the maximum number of distinct irreducible constituents of degree coprime to $p$ of restrictions of irreducible characters of $\mathfrak{S}_n$ …
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On Proofs of Sylow's Theorem
We give five proofs of Sylow's Theorem. The proofs given will be Sylow's original proof, the Cauchy-Frobenius proof using double cosets, Frobenius' proof (two versions) using the class equation, and Wielandt's proof using subsets. We give a number of different examples to illustrate the various …
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Finite Groups Acting on Sets With Applications
… Polya-Burnside Theorem, and the First and Second Sylow Theorems. The purpose or aim of this thesis is to give the mathematical proofs and solutions to the selected propositions. However, it will be assumed that the reader has had a first course in modern algebra. Finite groups acting on sets is a …
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A Characterization of the Four Dimensional Projective Special Linear Group Psl(5,3) Over the Field of Three Elements by the Centralizer of an Involution Contained in the Center of A Sylow 2-Subgroup
Made available in DSpace on 2014-12-11T18:23:50Z (GMT). No. of bitstreams: 1 7219870.pdf: 1808081 bytes, checksum: 0905db1d919380f22ad2998659d03da9 (MD5) Previous issue date: 1972
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Orders of Perfect Groups with Dihedral Involution Centralizers
… is true in each case that this centralizer is a Sylow 2-subgroup of G. We then use character-theoretic techniques to generate a list of possibilities for the order of G. In the process of generating this list of possible orders, we prove several results about the structure of our group under …