Date of Award
2008
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Abstract
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.
Extent
vii, 104 leaves : ill.
Recommended Citation
Bozovic, Vladimir., "Algebraic and combinatorial aspects of group factorizations" (2008). Electronic Theses and Dissertations 2000 - 2009. 1402.
https://digitalcommons.fau.edu/etd_general_5/1402
Identifier
FADT107805
Comments
by Vladimir Bozovic.|Thesis (Ph.D.)--Florida Atlantic University, 2008.|Includes bibliography.|Electronic reproduction. Boca Raton, FL : 2008 Mode of access: World Wide Web.|by Vladimir Bozovic.