Dihedralizing the Quaternions

In this paper, we will take the classic dihedral and quaternion groups and explore questions like "what if we replace i = e2πi/4 in Q8 with a larger root of unity?" and "what if we add a reflection to Q8?" The delightful answers reveal lesser-known families like the dicyclic, diq...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	The American mathematical monthly 2024-04, Vol.131 (4), p.294-308
1. Verfasser:	Macauley, Matthew
Format:	Artikel
Sprache:	eng
Schlagworte:	Graph theory Graphs Lattices Lie groups Mathematics Mathematics education Quaternions Subgroups
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	308
container_issue	4
container_start_page	294
container_title	The American mathematical monthly
container_volume	131
creator	Macauley, Matthew
description	In this paper, we will take the classic dihedral and quaternion groups and explore questions like "what if we replace i = e2πi/4 in Q8 with a larger root of unity?" and "what if we add a reflection to Q8?" The delightful answers reveal lesser-known families like the dicyclic, diquaternion, semidihedral, and semiabelian groups, which come to life with visuals such as Cayley graphs, cycle graphs, and subgroup lattices.
doi_str_mv	10.1080/00029890.2023.2298656
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3030820061</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3030820061</sourcerecordid><originalsourceid>FETCH-LOGICAL-c276t-3a67a0ef4ab79a2b32f14aa9fe6af1148135c10cb5202367778e5229e8014f453</originalsourceid><addsrcrecordid>eNo1kE1Lw0AQhhdRMFZ_QqHgOXVmv_co9RMKIuh5mcRdm1KTupsc9Neb0HqaGXiY9-VhbI6wRLBwAwDcWQdLDlws-bhrpU9YgU5ACc7wU1ZMTDlB5-wi5-14gpK8YPO7ZhM-Eu2a36b9XPSbsHgdqA-pbbo2X7KzSLscro5zxt4f7t9WT-X65fF5dbsua250XwrShiBESZVxxCvBI0oiF4OmiCgtClUj1JWaGmpjjA1q7BksoIxSiRm7Pvzdp-57CLn3225I7RjpBQiwHEDjSKkDVacu5xSi36fmi9KPR_CTCf9vwk85_mhC_AEKR04j</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3030820061</pqid></control><display><type>article</type><title>Dihedralizing the Quaternions</title><source>Alma/SFX Local Collection</source><creator>Macauley, Matthew</creator><creatorcontrib>Macauley, Matthew</creatorcontrib><description>In this paper, we will take the classic dihedral and quaternion groups and explore questions like "what if we replace i = e2πi/4 in Q8 with a larger root of unity?" and "what if we add a reflection to Q8?" The delightful answers reveal lesser-known families like the dicyclic, diquaternion, semidihedral, and semiabelian groups, which come to life with visuals such as Cayley graphs, cycle graphs, and subgroup lattices.</description><identifier>ISSN: 0002-9890</identifier><identifier>EISSN: 1930-0972</identifier><identifier>DOI: 10.1080/00029890.2023.2298656</identifier><language>eng</language><publisher>Washington: Taylor & Francis Ltd</publisher><subject>Graph theory ; Graphs ; Lattices ; Lie groups ; Mathematics ; Mathematics education ; Quaternions ; Subgroups</subject><ispartof>The American mathematical monthly, 2024-04, Vol.131 (4), p.294-308</ispartof><rights>Copyright Taylor & Francis Ltd. Apr 2024</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c276t-3a67a0ef4ab79a2b32f14aa9fe6af1148135c10cb5202367778e5229e8014f453</cites><orcidid>0000-0002-4409-2248</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,777,781,27905,27906</link.rule.ids></links><search><creatorcontrib>Macauley, Matthew</creatorcontrib><title>Dihedralizing the Quaternions</title><title>The American mathematical monthly</title><description>In this paper, we will take the classic dihedral and quaternion groups and explore questions like "what if we replace i = e2πi/4 in Q8 with a larger root of unity?" and "what if we add a reflection to Q8?" The delightful answers reveal lesser-known families like the dicyclic, diquaternion, semidihedral, and semiabelian groups, which come to life with visuals such as Cayley graphs, cycle graphs, and subgroup lattices.</description><subject>Graph theory</subject><subject>Graphs</subject><subject>Lattices</subject><subject>Lie groups</subject><subject>Mathematics</subject><subject>Mathematics education</subject><subject>Quaternions</subject><subject>Subgroups</subject><issn>0002-9890</issn><issn>1930-0972</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNo1kE1Lw0AQhhdRMFZ_QqHgOXVmv_co9RMKIuh5mcRdm1KTupsc9Neb0HqaGXiY9-VhbI6wRLBwAwDcWQdLDlws-bhrpU9YgU5ACc7wU1ZMTDlB5-wi5-14gpK8YPO7ZhM-Eu2a36b9XPSbsHgdqA-pbbo2X7KzSLscro5zxt4f7t9WT-X65fF5dbsua250XwrShiBESZVxxCvBI0oiF4OmiCgtClUj1JWaGmpjjA1q7BksoIxSiRm7Pvzdp-57CLn3225I7RjpBQiwHEDjSKkDVacu5xSi36fmi9KPR_CTCf9vwk85_mhC_AEKR04j</recordid><startdate>20240420</startdate><enddate>20240420</enddate><creator>Macauley, Matthew</creator><general>Taylor & Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><orcidid>https://orcid.org/0000-0002-4409-2248</orcidid></search><sort><creationdate>20240420</creationdate><title>Dihedralizing the Quaternions</title><author>Macauley, Matthew</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c276t-3a67a0ef4ab79a2b32f14aa9fe6af1148135c10cb5202367778e5229e8014f453</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Graph theory</topic><topic>Graphs</topic><topic>Lattices</topic><topic>Lie groups</topic><topic>Mathematics</topic><topic>Mathematics education</topic><topic>Quaternions</topic><topic>Subgroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Macauley, Matthew</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The American mathematical monthly</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Macauley, Matthew</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dihedralizing the Quaternions</atitle><jtitle>The American mathematical monthly</jtitle><date>2024-04-20</date><risdate>2024</risdate><volume>131</volume><issue>4</issue><spage>294</spage><epage>308</epage><pages>294-308</pages><issn>0002-9890</issn><eissn>1930-0972</eissn><abstract>In this paper, we will take the classic dihedral and quaternion groups and explore questions like "what if we replace i = e2πi/4 in Q8 with a larger root of unity?" and "what if we add a reflection to Q8?" The delightful answers reveal lesser-known families like the dicyclic, diquaternion, semidihedral, and semiabelian groups, which come to life with visuals such as Cayley graphs, cycle graphs, and subgroup lattices.</abstract><cop>Washington</cop><pub>Taylor & Francis Ltd</pub><doi>10.1080/00029890.2023.2298656</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0002-4409-2248</orcidid><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	ISSN: 0002-9890
ispartof	The American mathematical monthly, 2024-04, Vol.131 (4), p.294-308
issn	0002-9890 1930-0972
language	eng
recordid	cdi_proquest_journals_3030820061
source	Alma/SFX Local Collection
subjects	Graph theory Graphs Lattices Lie groups Mathematics Mathematics education Quaternions Subgroups
title	Dihedralizing the Quaternions
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T08%3A05%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Dihedralizing%20the%20Quaternions&rft.jtitle=The%20American%20mathematical%20monthly&rft.au=Macauley,%20Matthew&rft.date=2024-04-20&rft.volume=131&rft.issue=4&rft.spage=294&rft.epage=308&rft.pages=294-308&rft.issn=0002-9890&rft.eissn=1930-0972&rft_id=info:doi/10.1080/00029890.2023.2298656&rft_dat=%3Cproquest_cross%3E3030820061%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3030820061&rft_id=info:pmid/&rfr_iscdi=true