dc.contributor.author Goodwin, Simon M. dc.contributor.author Mosch, Peter dc.contributor.author Röhrle, Gerhard dc.date.accessioned 2013-04-10T12:00:02Z dc.date.accessioned 2016-10-05T14:13:54Z dc.date.available 2013-04-10T12:00:02Z dc.date.available 2016-10-05T14:13:54Z dc.date.issued 2013-04-10 dc.identifier.uri http://publications.mfo.de/handle/mfo/1060 dc.description Research in Pairs 2012 en_US dc.description.abstract Let $G(q)$ be a finite Chevalley group, where $q$ is a power of a good prime $p$, and let $U(q)$ be a Sylow $p$-subgroup of $G(q)$. Then a generalized version of a conjecture of Higman asserts that the number $k(U(q))$ of conjugacy classes in $U(q)$ is given by a polynomial in $q$ with integer coefficients. In [12], the first and the third authors developed an algorithm to calculate the values of $k(U(q))$. By implementing it into a computer program using GAP, they were able to calculate $k(U(q))$ for $G$ of rank at most 5, thereby proving that for these cases $k(U(q))$ is given by a polynomial in $q$. In this paper we present some refinements and improvements of the algorithm that allow us to calculate the values of $k(U(q))$ for finite Chevalley groups of rank six and seven, except $E_7$. We observe that $k(U(q))$ is a polynomial, so that the generalized Higman conjecture holds for these groups. Moreover, if we write $k(U(q))$ as a polynomial in $q-1$, then the coefficients are non-negative. Under the assumption that $k(U(q))$ is a polynomial in $q-1$, we also give an explicit formula for the coefficients of $k(U(q))$ of degrees zero, one and two. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2013,10 dc.subject Finite Chevalley Groups en_US dc.subject Sylow Subgroups en_US dc.subject Conjugacy Classes en_US dc.title Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and seven en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2013-10 local.scientificprogram Research in Pairs 2012 local.series.id OWP-2013-10 local.subject.msc 20
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