https://en.formulasearchengine.com/w/index.php?action=history&feed=atom&title=Catalecticant Catalecticant - Revision history 2026-08-03T07:45:42Z Revision history for this page on the wiki MediaWiki 1.47.0-wmf.7 https://en.formulasearchengine.com/w/index.php?title=Catalecticant&diff=26202&oldid=prev en>R.e.b.: Spelling/grammar correction 2012-05-11T15:33:40Z <p>Spelling/grammar correction</p> <p><b>New page</b></p><div>In the [[mathematics|mathematical]] field of [[group theory]], the &#039;&#039;&#039;Nottingham group&#039;&#039;&#039; is the group &#039;&#039;J&#039;&#039;(&#039;&#039;&#039;F&#039;&#039;&#039;&lt;sub&gt;&#039;&#039;p&#039;&#039;&lt;/sub&gt;) or &#039;&#039;N&#039;&#039;(&#039;&#039;&#039;F&#039;&#039;&#039;&lt;sub&gt;&#039;&#039;p&#039;&#039;&lt;/sub&gt;) consisting of formal [[power series]] &#039;&#039;t&#039;&#039; + &#039;&#039;a&#039;&#039;&lt;sub&gt;2&lt;/sub&gt;&#039;&#039;t&#039;&#039;&lt;sup&gt;2&lt;/sup&gt;+...<br /> with coefficients in &#039;&#039;&#039;F&#039;&#039;&#039;&lt;sub&gt;&#039;&#039;p&#039;&#039;&lt;/sup&gt;. The group multiplication is given by formal composition also called substitution. That is, if<br /> :&lt;math&gt;<br /> f = t+ \sum_{n=2}^\infty a_n t^n<br /> &lt;/math&gt;<br /> and if &lt;math&gt;g&lt;/math&gt; is another element, then <br /> :&lt;math&gt;gf = f(g) = g+ \sum_{n=2}^\infty a_n g^n&lt;/math&gt;. <br /> Notably, the group multiplication is not [[abelian group|abelian]]. The group was studied by {{harvtxt|Johnson|1988}} and the name &quot;Nottingham group&quot; refers to Johnson&#039;s former domicile. It is a finitely generated pro-&#039;&#039;p&#039;&#039;-group.<br /> <br /> ==See also==<br /> *[[Fesenko group]]<br /> <br /> ==References==<br /> <br /> *{{Citation | last1=Camina | first1=Rachel | editor1-last=Sautoy | editor1-first=Marcus Du | editor2-last=Segal | editor2-first=Dan | editor3-last=Shalev | editor3-first=Aner | title=New horizons in pro-p groups | url=http://books.google.com/books?isbn=0817641718 | publisher=Birkhäuser Boston | location=Boston, MA | series=Progr. Math. | isbn=978-0-8176-4171-9 | mr=1765121 | year=2000 | volume=184 | chapter=The Nottingham group | pages=205–221}}<br /> *{{Citation | last1=Johnson | first1=D. L. | title=The group of formal power series under substitution | url=http://anziamj.austms.org.au/JAMSA/V45/Part3/Johnson.html | mr=957195 | year=1988 | journal=Australian Mathematical Society. Journal. Series A. Pure Mathematics and Statistics | issn=0263-6115 | volume=45 | issue=3 | pages=296–302}}<br /> <br /> [[Category:Group theory]]</div> en>R.e.b.