A short survey on Coclass Graphs

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

Leedham-Green & Newman [11] defined the coclass of a p-group of order pn and nilpotency class c as r = n−c. The investigation of the p-groups of a fixed coclass led to deep results in p-group theory (see the book of Leedham-Green & McKay), applications (see for example [1, 12]), and generalisations to other algebraic objects (see for example [5, 8]). In the last decade, the focus in coclass theory is on the investigation of the coclass graph G(p, r) associated with the finite p-groups of coclass r. It is conjectured that this infinite graph can be described by a finite subgraph and several “periodic patterns”. The aim of this talk is to give a survey on the known periodicity results, the outstanding problems, and a recent new result for the graph G(p, 1). Some details are given below.
Original languageEnglish
Title of host publicationMathematisches Forschungsinstitut Oberwolfach
Subtitle of host publicationReport No. 37/2016 - Computational Group Theory
Place of PublicationGermany
PublisherMathematisches Forschungsinstitut Oberwolfach
Pages2140-2141
Number of pages2
Volume37/2016
Publication statusPublished - 2016
EventComputational Group Theory, 2016 - Oberwolfach, Germany
Duration: 31 Jul 20166 Aug 2016
Conference number: 7th

Conference

ConferenceComputational Group Theory, 2016
CountryGermany
Period31/07/166/08/16

Cite this

Dietrich, H. (2016). A short survey on Coclass Graphs. In Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2016 - Computational Group Theory (Vol. 37/2016, pp. 2140-2141). Germany: Mathematisches Forschungsinstitut Oberwolfach.
Dietrich, Heiko. / A short survey on Coclass Graphs. Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2016 - Computational Group Theory. Vol. 37/2016 Germany : Mathematisches Forschungsinstitut Oberwolfach, 2016. pp. 2140-2141
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Dietrich, H 2016, A short survey on Coclass Graphs. in Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2016 - Computational Group Theory. vol. 37/2016, Mathematisches Forschungsinstitut Oberwolfach, Germany, pp. 2140-2141, Computational Group Theory, 2016, Germany, 31/07/16.

A short survey on Coclass Graphs. / Dietrich, Heiko.

Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2016 - Computational Group Theory. Vol. 37/2016 Germany : Mathematisches Forschungsinstitut Oberwolfach, 2016. p. 2140-2141.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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AB - Leedham-Green & Newman [11] defined the coclass of a p-group of order pn and nilpotency class c as r = n−c. The investigation of the p-groups of a fixed coclass led to deep results in p-group theory (see the book of Leedham-Green & McKay), applications (see for example [1, 12]), and generalisations to other algebraic objects (see for example [5, 8]). In the last decade, the focus in coclass theory is on the investigation of the coclass graph G(p, r) associated with the finite p-groups of coclass r. It is conjectured that this infinite graph can be described by a finite subgraph and several “periodic patterns”. The aim of this talk is to give a survey on the known periodicity results, the outstanding problems, and a recent new result for the graph G(p, 1). Some details are given below.

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Dietrich H. A short survey on Coclass Graphs. In Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2016 - Computational Group Theory. Vol. 37/2016. Germany: Mathematisches Forschungsinstitut Oberwolfach. 2016. p. 2140-2141