Profinite groups with few conjugacy classes of p-elements

It is proved that a profinite group G has fewer than 2^{\aleph _0} conjugacy classes of p-elements for an odd prime p if and only if its p-Sylow p-subgroups are finite. (Here, by a p-element one understands an element that either has p-power order or topologically generates a group isomorphic to \ma...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Proceedings of the American Mathematical Society 2022-08, Vol.150 (8), p.3297
1. Verfasser:	John S. Wilson
Format:	Artikel
Sprache:	eng
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page
container_issue	8
container_start_page	3297
container_title	Proceedings of the American Mathematical Society
container_volume	150
creator	John S. Wilson
description	It is proved that a profinite group G has fewer than 2^{\aleph _0} conjugacy classes of p-elements for an odd prime p if and only if its p-Sylow p-subgroups are finite. (Here, by a p-element one understands an element that either has p-power order or topologically generates a group isomorphic to \mathbb {Z}_p.) A weaker result is proved for p=2.
doi_str_mv	10.1090/proc/15925
format	Article
fullrecord	<record><control><sourceid>ams</sourceid><recordid>TN_cdi_ams_primary_10_1090_proc_15925</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1090_proc_15925</sourcerecordid><originalsourceid>FETCH-LOGICAL-a185t-2c69e326033bf08438f5250b03d49aa7279fe20ef011a0d069bca177a651fc483</originalsourceid><addsrcrecordid>eNotz01LAzEUheEgCo7Vjb8gG5ex9yaTTLKU4hcUdKHr4U6a1CnzRTKl9N9r1dXh3Rx4GLtFuEdwsJzS6JeondRnrECwVhgrzTkrAEAK55S7ZFc5734SXVkVzL2nMbZDOwe-TeN-yvzQzl88hgP347Dbb8kfue8o55D5GPkkQhf6MMz5ml1E6nK4-d8F-3x6_Fi9iPXb8-vqYS0IrZ6F9MYFJQ0o1USwpbJRSw0NqE3piCpZuRgkhAiIBBswrvGEVUVGY_SlVQt29_dLfa6n1PaUjjVCffLWJ2_961XfgshH_w</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Profinite groups with few conjugacy classes of p-elements</title><source>American Mathematical Society Publications</source><creator>John S. Wilson</creator><creatorcontrib>John S. Wilson</creatorcontrib><description>It is proved that a profinite group G has fewer than 2^{\aleph _0} conjugacy classes of p-elements for an odd prime p if and only if its p-Sylow p-subgroups are finite. (Here, by a p-element one understands an element that either has p-power order or topologically generates a group isomorphic to \mathbb {Z}_p.) A weaker result is proved for p=2.</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><identifier>DOI: 10.1090/proc/15925</identifier><language>eng</language><ispartof>Proceedings of the American Mathematical Society, 2022-08, Vol.150 (8), p.3297</ispartof><rights>Copyright 2022, American Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ams.org/proc/2022-150-08/S0002-9939-2022-15925-5/S0002-9939-2022-15925-5.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttps://www.ams.org/proc/2022-150-08/S0002-9939-2022-15925-5/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>68,314,780,784,23328,27924,27925,77836,77846</link.rule.ids></links><search><creatorcontrib>John S. Wilson</creatorcontrib><title>Profinite groups with few conjugacy classes of p-elements</title><title>Proceedings of the American Mathematical Society</title><description>It is proved that a profinite group G has fewer than 2^{\aleph _0} conjugacy classes of p-elements for an odd prime p if and only if its p-Sylow p-subgroups are finite. (Here, by a p-element one understands an element that either has p-power order or topologically generates a group isomorphic to \mathbb {Z}_p.) A weaker result is proved for p=2.</description><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNotz01LAzEUheEgCo7Vjb8gG5ex9yaTTLKU4hcUdKHr4U6a1CnzRTKl9N9r1dXh3Rx4GLtFuEdwsJzS6JeondRnrECwVhgrzTkrAEAK55S7ZFc5734SXVkVzL2nMbZDOwe-TeN-yvzQzl88hgP347Dbb8kfue8o55D5GPkkQhf6MMz5ml1E6nK4-d8F-3x6_Fi9iPXb8-vqYS0IrZ6F9MYFJQ0o1USwpbJRSw0NqE3piCpZuRgkhAiIBBswrvGEVUVGY_SlVQt29_dLfa6n1PaUjjVCffLWJ2_961XfgshH_w</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>John S. Wilson</creator><scope/></search><sort><creationdate>20220801</creationdate><title>Profinite groups with few conjugacy classes of p-elements</title><author>John S. Wilson</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a185t-2c69e326033bf08438f5250b03d49aa7279fe20ef011a0d069bca177a651fc483</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>John S. Wilson</creatorcontrib><jtitle>Proceedings of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>John S. Wilson</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Profinite groups with few conjugacy classes of p-elements</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><date>2022-08-01</date><risdate>2022</risdate><volume>150</volume><issue>8</issue><spage>3297</spage><pages>3297-</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><abstract>It is proved that a profinite group G has fewer than 2^{\aleph _0} conjugacy classes of p-elements for an odd prime p if and only if its p-Sylow p-subgroups are finite. (Here, by a p-element one understands an element that either has p-power order or topologically generates a group isomorphic to \mathbb {Z}_p.) A weaker result is proved for p=2.</abstract><doi>10.1090/proc/15925</doi><tpages>9</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 0002-9939
ispartof	Proceedings of the American Mathematical Society, 2022-08, Vol.150 (8), p.3297
issn	0002-9939 1088-6826
language	eng
recordid	cdi_ams_primary_10_1090_proc_15925
source	American Mathematical Society Publications
title	Profinite groups with few conjugacy classes of p-elements
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T00%3A17%3A26IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ams&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Profinite%20groups%20with%20few%20conjugacy%20classes%20of%20p-elements&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.au=John%20S.%20Wilson&rft.date=2022-08-01&rft.volume=150&rft.issue=8&rft.spage=3297&rft.pages=3297-&rft.issn=0002-9939&rft.eissn=1088-6826&rft_id=info:doi/10.1090/proc/15925&rft_dat=%3Cams%3E10_1090_proc_15925%3C/ams%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true