Every (k+1)-affine complete nilpotent group of class k is affine complete

Erhard Aichinger; Jürgen Fuß

doi:10.1142/S0218196706002858

Every (k+1)-affine complete nilpotent group of class k is affine complete

Erhard Aichinger, Jürgen Fuß

Research Center Hagenberg

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We let G be a group, and we let k be a natural number. We assume that G is nilpotent of class at most k, and that every (k + 1)-ary congruence preserving function on G is a polynomial function. We show that then every congruence preserving function on G (of any finite arity) is a polynomial function.

Original language	English
Article number	2
Pages (from-to)	259-274
Number of pages	16
Journal	International Journal of Algebra and Computation
Volume	16
Issue number	2
DOIs	https://doi.org/10.1142/S0218196706002858
Publication status	Published - Apr 2006

Keywords

Affine completeness
Commutator collection
Congruence preserving functions
Nilpotent groups
Polynomial completeness

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10.1142/S0218196706002858

Cite this

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title = "Every (k+1)-affine complete nilpotent group of class k is affine complete",

abstract = "We let G be a group, and we let k be a natural number. We assume that G is nilpotent of class at most k, and that every (k + 1)-ary congruence preserving function on G is a polynomial function. We show that then every congruence preserving function on G (of any finite arity) is a polynomial function.",

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AU - Aichinger, Erhard

AU - Fuß, Jürgen

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N2 - We let G be a group, and we let k be a natural number. We assume that G is nilpotent of class at most k, and that every (k + 1)-ary congruence preserving function on G is a polynomial function. We show that then every congruence preserving function on G (of any finite arity) is a polynomial function.

AB - We let G be a group, and we let k be a natural number. We assume that G is nilpotent of class at most k, and that every (k + 1)-ary congruence preserving function on G is a polynomial function. We show that then every congruence preserving function on G (of any finite arity) is a polynomial function.

KW - Affine completeness

KW - Commutator collection

KW - Congruence preserving functions

KW - Nilpotent groups

KW - Polynomial completeness

UR - https://www.scopus.com/pages/publications/33646504859

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DO - 10.1142/S0218196706002858

M3 - Article

SN - 0218-1967

VL - 16

SP - 259

EP - 274

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 2

M1 - 2

ER -

Every (k+1)-affine complete nilpotent group of class k is affine complete

Abstract

Keywords

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