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

Institute for Algebra

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

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 $p^4$ is determined as an application.

Original language	English
Title of host publication	Contributions to General Algebra
Number of pages	5
Volume	10
Publication status	Published - Apr 1998

Fields of science

101001 Algebra

Computing with Near-rings - Algorithms and Implementation
Binder, F. (Researcher), Boykett, T. (Researcher), Ecker, J. (Researcher), Eggetsberger, R. (Researcher), Nöbauer, C. (Researcher) & Pilz, G. (PI)
FWF
01.07.1996 → 31.01.1998
Project: Funded research › FWF - Austrian Science Fund

Cite this

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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 $p^4$ is determined as an application.",

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AU - Ecker, Juergen

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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

Fields of science

Projects

Computing with Near-rings - Algorithms and Implementation

Cite this