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dc.contributor.authorGoodwin, Simon M.
dc.contributor.authorMosch, Peter
dc.contributor.authorRöhrle, Gerhard
dc.date.accessioned2013-04-10T12:00:02Z
dc.date.accessioned2016-10-05T14:13:54Z
dc.date.available2013-04-10T12:00:02Z
dc.date.available2016-10-05T14:13:54Z
dc.date.issued2013-04-10
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1060
dc.descriptionResearch in Pairs 2012en_US
dc.description.abstractLet $G(q)$ 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.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2013,10
dc.subjectFinite Chevalley Groupsen_US
dc.subjectSylow Subgroupsen_US
dc.subjectConjugacy Classesen_US
dc.titleCalculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and sevenen_US
dc.typePreprinten_US
dc.rights.licenseDieses 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.licenseThis 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.doi10.14760/OWP-2013-10
local.scientificprogramResearch in Pairs 2012
local.series.idOWP-2013-10
local.subject.msc20
dc.identifier.urnurn:nbn:de:101:1-2024031912382609811787
dc.identifier.ppn1652237542


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