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1 
Asymptotics of some number theoretic functions and an application to the growth of nilpotent groupsStoll, Michael. January 1994 (has links)
Thesis (doctoral)Universität Bonn, 1993. / Includes bibliographical references (p. 67).

2 
Locally nilpotent 5Engel pgroupsMilian, Dagmara January 2010 (has links)
In this thesis we investigate the structure of locally nilpotent 5Engel pgroups. We show that for p > 7, locally nilpotent 5Engel pgroups have class at most 10. This is a global theorem, where the result is not dependent on the number of generators of the group. The proof uses new and established Lie methods and a custom C++ implementation of an algorithm that constructs minimal generating sets and structure constants of multi graded Lie algebras in a variety defined by three multilinear relations, which hold in the Lie rings associated with 5Engel pgroups. We obtain our results by calculating in the set Q(p) = {~ I x E Z, yE Z+, Y # 0 modulo any p f/. p} (where p is a set of excluded primes and x, y are arbitrarily large integers), as well as the fields Zp, p prime. We introduce several reduction theorems, making the result possible. We also present results about the normal closure of elements in these groups. We use a Higman reduction theorem and the same custom C++ program to show that locally nilpotent 5Engel pgroups, p 2: 5, are Fitting, with Fitting degree at most 4 if p > 7, at most 5 if p = 7 and at most 6 if p = 5. These results are best possible.

3 
Right Engel subgroupsCrosby, Peter January 2011 (has links)
In this thesis we find deep results on the structure of normal right nEngel subgroups that are contained in some term of the upper central series of a group. We start with some known results, and one new result, on the structure of locally nilpotent nEngel groups. These are closely related to the solution of the restricted Burnside problem. We also give specific details of the structure of 2Engel and 3Engel groups in the context of these results. The main idea of this thesis is to generalise these results to apply to normal upper central right nEngel subgroups. We also consider the special case of locally finite pgroups and again generalise some deep results on the structure of nEngel such groups to apply to right nEngel subgroups. For each of the theorems on right nEngel subgroups, complete details are given for the case n = 2. Right 3Engel subgroups have a more complicated structure. For these we prove a Fitting result, for which we exclude the prime 3, and using this we also find a sharp bound on the upper central degree in the torsionfree case. In fact we only need to exclude the primes 2, 3 and 5 for this result. This gives some further information on the structure of right 3Engel subgroups in the context of the main theorems.

4 
The large scale geometry of nilpotentbycycle groups /Ahlin, Ashley Reiter. January 2002 (has links)
Thesis (Ph. D.)University of Chicago, Department of Mathematics, June 2002. / Includes bibliographical references. Also available on the Internet.

5 
Zur Rationalität polynomialer WachstumsfunktionenWeber, Bernhard. January 1989 (has links)
Thesis (doctoral)Universität Bonn, 1988. / Includes bibliographical references.

6 
Geometric and analytic properties in the behavior of random walks on nilpotent covering graphsIshiwata, Satoshi. January 1900 (has links)
Thesis (Ph. D.)Tohoku University, 2004. / "June 2004." Includes bibliographical references (p. 6972).

7 
Locally Nilpotent Derivations and Their QuasiExtensionsChitayat, Michael January 2016 (has links)
In this thesis, we introduce the theory of locally nilpotent derivations and use it to compute certain ring invariants.
We prove some results about quasiextensions of derivations and use them to show that certain rings are nonrigid.
Our main result states that if k is a field of characteristic zero, C is an affine kdomain and
B = C[T,Y] / < T^nY  f(T) >, where n >= 2 and f(T) \in C[T] is such that
delta^2(f(0)) != 0 for all nonzero locally nilpotent derivations delta of C,
then ML(B) != k.
This shows in particular that the ring B is not a polynomial ring over k.

8 
An Introduction to Lie AlgebraTalley, Amanda Renee 01 December 2017 (has links)
An (associative) algebra is a vector space over a field equipped with an associative, bilinear multiplication. By use of a new bilinear operation, any associative algebra morphs into a nonassociative abstract Lie algebra, where the new product in terms of the given associative product, is the commutator. The crux of this paper is to investigate the commutator as it pertains to the general linear group and its subalgebras. This forces us to examine properties of ring theory under the lens of linear algebra, as we determine subalgebras, ideals, and solvability as decomposed into an extension of abelian ideals, and nilpotency, as decomposed into the lower central series and eventual zero subspace. The map sending the Lie algebra L to a derivation of L is called the adjoint representation, where a given Lie algebra is nilpotent if and only if the adjoint is nilpotent. Our goal is to prove Engel's Theorem, which states that if all elements of L are adnilpotent, then L is nilpotent.

9 
Classification of Nilpotent Lie Algebras of Dimension 7 (over Algebraically Closed Field and R)Gong, MingPeng January 1998 (has links)
This thesis is concerned with the classification of 7dimensional nilpotent Lie algebras. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension <i>n</i> given those algebras of dimension < <i>n</i>, and their automorphism groups. By using this method, we construct all nonisomorphic 7dimensional nilpotent Lie algebras in the following two cases: (1) over an algebraically closed field of arbitrary characteristic except 2; (2) over the real field <strong>R</strong>. We have compared our lists with three of the most recent lists (those of Seeley, AncocheaGoze, and Romdhani). While our list in case (1) over <strong>C</strong> differs greatly from that of AncocheaGoze, which contains too many errors to be usable, it agrees with that of Seeley apart from a few corrections that should be made in his list, Our list in case (2) over <strong>R</strong> contains all the algebras on Romdhani's list, which omits many algebras.

10 
Classification of Nilpotent Lie Algebras of Dimension 7 (over Algebraically Closed Field and R)Gong, MingPeng January 1998 (has links)
This thesis is concerned with the classification of 7dimensional nilpotent Lie algebras. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension <i>n</i> given those algebras of dimension < <i>n</i>, and their automorphism groups. By using this method, we construct all nonisomorphic 7dimensional nilpotent Lie algebras in the following two cases: (1) over an algebraically closed field of arbitrary characteristic except 2; (2) over the real field <strong>R</strong>. We have compared our lists with three of the most recent lists (those of Seeley, AncocheaGoze, and Romdhani). While our list in case (1) over <strong>C</strong> differs greatly from that of AncocheaGoze, which contains too many errors to be usable, it agrees with that of Seeley apart from a few corrections that should be made in his list, Our list in case (2) over <strong>R</strong> contains all the algebras on Romdhani's list, which omits many algebras.

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