Group covers and partitions : covering and partition numbers
- WCU Author/Contributor (non-WCU co-authors, if there are any, appear on document)
- Nicholas Sizemore (Creator)
- Institution
- Western Carolina University (WCU )
- Web Site: http://library.wcu.edu/
- Advisor
- Tuval Foguel
Abstract: A group cover is a collection of subgroups whose union is the group. A group partition
is a group cover in which the elements have trivial pairwise intersection. Previous
work has been done to investigate properties related to the covering number of a
group - the minimal number of subgroups necessary to forma cover. Here we define
analogously the partition number of a group and examine some of its properties, including
its relation to the covering number. In particular, we provide a classification
of the covering and partition numbers of the dihedral groups. Also presented is a
result concerning a minimal partition of the symmetric group on four elements.
Further, we utilize GAP to provide some computational methods for studying partition
numbers. Code samples are provided to test conditions relevant to partitions
and the partition number; specifically, we are able to use GAP to help verify various
conjectures about partitions of small finite groups. Included is a naïve and computationally
intense method to find the partition number, as well as an attempted refinement
designed to deal with the inefficiency of the naïve method.
Group covers and partitions : covering and partition numbers
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Created on 3/1/2013
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Additional Information
- Publication
- Thesis
- Language: English
- Date: 2013
- Keywords
- covering number, dihedral group, gap, group covers, group partitions, partition number
- Subjects
- Group theory
- Partitions (Mathematics)