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1 
On local formations of finite groups.January 2001 (has links)
by Lam Chak Ming. / Thesis (M.Phil.)Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 7679). / Abstracts in English and Chinese. / Chapter 0  Introduction  p.5 / Chapter 1  Background Knowledge of Group Theory  p.7 / Chapter 1.1  Some Basic Results  p.7 / Chapter 1.2  Solvable Groups  p.13 / Chapter 1.3  Nilpotent groups and some useful results  p.15 / Chapter 2  Theory of Formations  p.21 / Chapter 2.1  Some Basic Results of Formations  p.21 / Chapter 2.2  Xcovering subgroups and Xprojectors  p.23 / Chapter 2.3  The Conjugacy of FCovering Subgroups  p.32 / Chapter 2.4  FNormalizers  p.36 / Chapter 3  Local Formations  p.47 / Chapter 3.1  The Construction of Local Formations  p.47 / Chapter 3.2  The Stability of Formations  p.51 / Chapter 3.3  The Complements of Fcoradicals  p.57 / Chapter 3.4  Minimal nonFgroups  p.59 / Chapter 4  Finite Groups With Given Minimal Subgroups  p.66 / Chapter 4.1  Cnormality of Groups  p.66 / Chapter 4.2  A Generalized Version of Ito's Theorem  p.70 / Bibliography  p.76

2 
Fabnormality and the theory of finite solvable groups.D'Arcy, Patrick David January 1971 (has links)
No description available.

3 
Character correspondence in finite groupsWolf, Thomas Roger. January 1977 (has links)
ThesisWisconsin. / Vita. Includes bibliographical references (leaf 100).

4 
pNormally embedded subgroups of finite soluble groupsChambers, Graham Anstruther, January 1969 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1969. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliography.

5 
Fabnormality and the theory of finite solvable groups.D'Arcy, Patrick David January 1971 (has links)
No description available.

6 
Symmetric colorings of finite groupsPhakathi, Jabulani 06 May 2015 (has links)
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. December 2014. / Let G be a finite group and let r ∈ N. A coloring of G is any mapping
: G −→ {1, 2, 3, ..., r}. Colorings of G, and are equivalent if there exists an
element g in G such that (xg−1) = (x) for all x in G. A coloring of a finite group
G is called symmetric with respect to an element g in G if (gx−1g) = (x) for all
x ∈ G. We derive formulae for computing the number of symmetric colorings and the
number of equivalence classes of symmetric colorings for some classes of finite groups

7 
FINITE GROUPS FOR WHICH EVERY COMPLEX REPRESENTATION IS REALIZABLE.WANG, KWANG SHANG. January 1985 (has links)
In Chapter 2 we develop the concept of total orthogonality. A number of necessary conditions are derived. Necessary and sufficient conditions for total orthogonality are obtained for 2groups and for split extensions of elementary abelian 2groups. A complete description is given for totally orthogonal groups whose character degrees are bounded by 2. Brauer's problem is reduced for Frobenius groups to the corresponding problems for Frobenius kernels and complements. In Chapter 3 classes of examples are presented illustrating the concepts and results of Chapter 2. It is shown, in particular, that 2Sylow subgroups of finite reflection groups, and of alternating groups, are totally orthogonal.

8 
On unipotent supports of reductive groups with a disconnected centreTaylor, Jonathan January 2012 (has links)
Let G be a connected reductive algebraic group defined over an algebraic closure of the finite field of prime order p > 0, which we assume to be good for G. We denote by F : G → G a Frobenius endomorphism of G and by G the corresponding Fqrational structure. If Irr(G) denotes the set of ordinary irreducible characters of G then by work of Lusztig and Geck we have a well defined map ΦG : Irr(G) → {Fstable unipotent conjugacy classes of G} where ΦG(χ) is the unipotent support of χ. Lusztig has given a classification of the irreducible characters of G and obtained their degrees. In particular he has shown that for each χ ∈ Irr(G) there exists an integer nχ such that nχ · χ(1) is a monic polynomial in q. Given a unipotent class O of G with representative u ∈ G we may define AG(u) to be the finite quotient group CG(u)/CG(u)◦. If the centre Z(G) is connected and G/Z(G) is simple then Lusztig and H´ezard have independently shown that for each Fstable unipotent class O of G there exists χ ∈ Irr(G) such that ΦG(χ) = O and nχ = AG(u), (in particular the map ΦG is surjective). The main result of this thesis extends this result to the case where G is any simple algebraic group, (hence removing the assumption that Z(G) is connected). In particular if G is simple we show that for each Fstable unipotent class O of G there exists χ ∈ Irr(G) such that ΦG(χ) = O and nχ = AG(u)F where u ∈ OF is a wellchosen representative. We then apply this result to prove, (for most simple groups), a conjecture of Kawanaka’s on generalised Gelfand–Graev representations (GGGRs). Namely that the GGGRs of G form a Zbasis for the Zmodule of all unipotently supported class functions of G. Finally we obtain an expression for a certain fourth root of unity associated to GGGRs in the case where G is a symplectic or special orthogonal group.

9 
Representations of quivers over finite fieldsHua, Jiuzhao , Mathematics & Statistics, Faculty of Science, UNSW January 1998 (has links)
The main purpose of this thesis is to obtain surprising identities by counting the representations of quivers over finite fields. A classical result states that the dimension vectors of the absolutely indecomposable representations of a quiver ?? are in onetoone correspondence with the positive roots of a root system ??, which is infinite in general. For a given dimension vector ?? ??? ??+, the number A??(??, q), which counts the isomorphism classes of the absolutely indecomposable representations of ?? of dimension ?? over the finite field Fq, turns out to be a polynomial in q with integer coefficients, which have been conjectured to be nonnegative by Kac. The main result of this thesis is a multivariable formal identity which expresses an infinite series as a formal product indexed by ??+ which has the coefficients of various polynomials A??(??, q) as exponents. This identity turns out to be a qanalogue of the remarkable WeylMacdonaldKac denominator identity modulus a conjecture of Kac, which asserts that the multiplicity of ?? is equal to the constant term of A??(??, q). An equivalent form of this conjecture is established and a partial solution is obtained. A new proof of the integrality of A??(??, q) is given. Three Maple programs have been included which enable one to calculate the polynomials A??(??, q) for quivers with at most three nodes. All sample outprints are consistence with Kac???s conjectures. Another result of this thesis is as follows. Let A be a finite dimensional algebra over a perfect field K, M be a finitely generated indecomposable module over A ???K ??K. Then there exists a unique indecomposable module M??? over A such that M is a direct summand of M??? ???K ??K, and there exists a positive integer s such that Ms = M ??? ?? ?? ?? ??? M (s copies) has a unique minimal field of definition which is isomorphic to the centre of End ??(M???) rad (End ??(M???)). If K is a finite field, then s can be taken to be 1.

10 
Subnormal structure of finite soluble groupsWetherell, Chris. January 2001 (has links)
No description available.

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