On the number of polynomial functions on nilpotent groups of class 2

Juergen Ecker

On the number of polynomial functions on nilpotent groups of class 2

Juergen Ecker

Institut für Algebra

Publikation: Beitrag in Buch/Bericht/Konferenzband › Konferenzbeitrag › Begutachtung

Abstract

Zur Bestimmung der Anzahl der Polynomfunktionen auf einer Gruppe der Nilpotenzklasse 2 kann eine gewisse Invariante er Gruppe, naemliche ihre Laenge (definiert von S. Scott) herangezogen werden. Wir geben scharfe Abschaetzungen fuer die Laenge einer Gruppe nach oben und nach unten und zeigen, wie die Laenge aus einer Praesentation der Gruppe abgelesen werden kann. Wir illustrieren diese Methode an den p-Gruppen der Ordnung hoechstens $p^4$.

Originalsprache	Englisch
Titel	Contributions to General Algebra
Seitenumfang	5
Band	10
Publikationsstatus	Veröffentlicht - Apr. 1998

Wissenschaftszweige

101001 Algebra

1 Abgeschlossen

Computing with Near-rings - Algorithms and Implementation
Binder, F. (Forscher*in), Boykett, T. (Forscher*in), Ecker, J. (Forscher*in), Eggetsberger, R. (Forscher*in), Nöbauer, C. (Forscher*in) & Pilz, G. (Projektleiter*in)
01.07.1996 → 31.01.1998
Projekt: Geförderte Forschung › FWF - Österreichischer Wissenschaftsfonds

Dieses zitieren

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title = "On the number of polynomial functions on nilpotent groups of class 2",

abstract = "In the case of a nilpotent group of class 2 a certain invariant of the group, the length defined by S. D. Scott can be used to determine the number of polynomial functions on the group. Sharp upper and lower bounds for this invariant are determined. It is shown how the length of a group can be determined from a set of generating elements and the length of all \$p\$-groups up to order \$p\textasciicircum{}4\$ is determined as an application.",

author = "Juergen Ecker",

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language = "English",

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booktitle = "Contributions to General Algebra",

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T1 - On the number of polynomial functions on nilpotent groups of class 2

AU - Ecker, Juergen

PY - 1998/4

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N2 - In the case of a nilpotent group of class 2 a certain invariant of the group, the length defined by S. D. Scott can be used to determine the number of polynomial functions on the group. Sharp upper and lower bounds for this invariant are determined. It is shown how the length of a group can be determined from a set of generating elements and the length of all $p$-groups up to order $p^4$ is determined as an application.

AB - In the case of a nilpotent group of class 2 a certain invariant of the group, the length defined by S. D. Scott can be used to determine the number of polynomial functions on the group. Sharp upper and lower bounds for this invariant are determined. It is shown how the length of a group can be determined from a set of generating elements and the length of all $p$-groups up to order $p^4$ is determined as an application.

M3 - Conference proceedings

SN - 3-85366-890-9

VL - 10

BT - Contributions to General Algebra

ER -

On the number of polynomial functions on nilpotent groups of class 2

Abstract

Wissenschaftszweige

Projekte

Computing with Near-rings - Algorithms and Implementation

Dieses zitieren