Character Tables of Metacyclic Groups

Character Tables of Metacyclic Groups

We show that any two split metacyclic groups with the same character tables are isomorphic. We then use this to show that among metacyclic groups that are either 2-groups or are of odd order divisible by at most two primes, that the dihedral and generalized quaternion groups of order 2^n, n = 3, are...

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Bibliographic Details
Main Author: Skabelund, Dane Christian
Format: Others
Published: BYU ScholarsArchive 2013
Subjects:
finite group
metacyclic group
split metacyclic group
character table
p-group
Mathematics
Online Access:https://scholarsarchive.byu.edu/etd/3913
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4912&context=etd
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spelling ndltd-BGMYU2-oai-scholarsarchive.byu.edu-etd-49122021-09-01T05:02:23Z Character Tables of Metacyclic Groups Skabelund, Dane Christian We show that any two split metacyclic groups with the same character tables are isomorphic. We then use this to show that among metacyclic groups that are either 2-groups or are of odd order divisible by at most two primes, that the dihedral and generalized quaternion groups of order 2^n, n = 3, are the only pairs that have the same character tables. 2013-03-11T07:00:00Z text application/pdf https://scholarsarchive.byu.edu/etd/3913 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4912&context=etd http://lib.byu.edu/about/copyright/ Theses and Dissertations BYU ScholarsArchive finite group metacyclic group split metacyclic group character table p-group Mathematics
collection NDLTD
format Others
sources NDLTD
topic finite group
metacyclic group
split metacyclic group
character table
p-group
Mathematics
spellingShingle finite group
metacyclic group
split metacyclic group
character table
p-group
Mathematics
Skabelund, Dane Christian
Character Tables of Metacyclic Groups
description We show that any two split metacyclic groups with the same character tables are isomorphic. We then use this to show that among metacyclic groups that are either 2-groups or are of odd order divisible by at most two primes, that the dihedral and generalized quaternion groups of order 2^n, n = 3, are the only pairs that have the same character tables.
author Skabelund, Dane Christian
author_facet Skabelund, Dane Christian
author_sort Skabelund, Dane Christian
title Character Tables of Metacyclic Groups
title_short Character Tables of Metacyclic Groups
title_full Character Tables of Metacyclic Groups
title_fullStr Character Tables of Metacyclic Groups
title_full_unstemmed Character Tables of Metacyclic Groups
title_sort character tables of metacyclic groups
publisher BYU ScholarsArchive
publishDate 2013
url https://scholarsarchive.byu.edu/etd/3913
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4912&context=etd
work_keys_str_mv AT skabelunddanechristian charactertablesofmetacyclicgroups
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