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Algebraic and combinatorial aspects of group factorizations

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Date Issued:
2008
Summary:
The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed.
Title: Algebraic and combinatorial aspects of group factorizations.
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Name(s): Bozovic, Vladimir.
Florida Atlantic University
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: multipart monograph
Date Issued: 2008
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: vii, 104 leaves : ill.
Language(s): English
Summary: The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed.
Identifier: 276769405 (oclc), 107805 (digitool), FADT107805 (IID), fau:2809 (fedora)
Note(s): by Vladimir Bozovic.
Thesis (Ph.D.)--Florida Atlantic University, 2008.
Includes bibliography.
Electronic reproduction. Boca Raton, FL : 2008 Mode of access: World Wide Web.
Subject(s): Physical measurements
Mapping (Mathematics)
Combinatorial enumeration problems
Algebra, Abstract
Held by: FBoU FABOC
Persistent Link to This Record: http://purl.flvc.org/FAU/107805
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU