Abstract

One of the basic facts of group theory is that each finite group contains a Sylow p -subgroup for each prime p which divides the order of the group. In this note we show that each vertex-transitive self- complementary graph has an analogous property. As a consequence of this fact, we obtain that each prime divisor p of the order of a vertex-transitive self-complementary graph satisfies the congruence p m ≡ 1(mod 4), where p m is the highest power of p which divides the order of the graph. 1991 Mathematics Subject Classification 05C25, 20B25. © London Mathematical Society « Previous | Next Article » Table of Contents This Article Bull. London Math. Soc. (1999) 31 (5): 531-533. doi: 10.1112/S0024609399005925 » Abstract Free Full Text (PDF) Free Classifications Notes and Papers Services Article metrics Alert me when cited Alert me if corrected Find similar articles Similar articles in Web of Science Add to my archive Download citation Citing Articles Load citing article information Citing articles via CrossRef Citing articles via Scopus Citing articles via Web of Science Citing articles via Google Scholar Google Scholar Articles by Muzychuk, M. Search for related content Related Content Load related web page information Share Email this article CiteULike Delicious Facebook Google+ Mendeley Twitter What's this? Search this journal: Advanced » Current Issue October 2015 47 (5) Alert me to new issues The Journal About the journal Rights & Permissions We are mobile – find out more Published on behalf of London Mathematical Society Impact Factor: 0.704 5-Yr impact factor: 0.764 Editors Peter Jørgensen Michael White View full editorial board LMS journals now available in full MathJax HTML. MathJax is an open-source JavaScript display engine that produces high-quality mathematics in all modern browsers. To learn more about MathJax, please visit their site at www.MathJax.org. For Authors Instructions to authors Including copyright assignment, and offprints order forms Alerting Services Email table of contents Email Advance Access CiteTrack XML RSS feed Corporate Services What we offer Advertising sales Reprints Supplements var taxonomies = ("SCI01480", "SCI01640", "SCI01790", "SCI02030"); Most Most Read Monstrous Moonshine Yutaka Taniyama and His Time: Very Personal Recollections A Report on Harmonic Maps Convexity and Commuting Hamiltonians The Geometries of 3-Manifolds » View all Most Read articles Most Cited Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces The Geometries of 3-Manifolds Convexity and Commuting Hamiltonians On the Number of Carmichael Numbers up to x Property T for von Neumann Algebras » View all Most Cited articles Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department. Online ISSN 1469-2120 - Print ISSN 0024-6093 Copyright © 2015 London Mathematical Society Oxford Journals Oxford University Press Site Map Privacy Policy Cookie Policy Legal Notices Frequently Asked Questions Other Oxford University Press sites: Oxford University Press Oxford Journals China Oxford Journals Japan Academic & Professional books Children's & Schools Books Dictionaries & Reference Dictionary of National Biography Digital Reference English Language Teaching Higher Education Textbooks International Education Unit Law Medicine Music Online Products & Publishing Oxford Bibliographies Online Oxford Dictionaries Online Oxford English Dictionary Oxford Language Dictionaries Online Oxford Scholarship Online Reference Rights and Permissions Resources for Retailers & Wholesalers Resources for the Healthcare Industry Very Short Introductions World's Classics var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); try { var pageTracker = _gat._getTracker("UA-189672-16"); pageTracker._setDomainName(".oxfordjournals.org"); pageTracker._trackPageview(); } catch(err) {}