An odd order group without the dimension property

Laurent Bartholdi; Roman Mikhailov

An odd order group without the dimension property

Group Theory 2021-01-14 v2

Authors: Laurent Bartholdi , Roman Mikhailov

Abstract

We construct a finitely presented group $G$ such that the $7$ th dimension quotient $G\cap(1+\varpi(\mathbb Z G)^7)/\gamma_7(G)$ has an element of order $3$ ; this immediately leads to a finite $3$ -group without the dimension property. This contradicts a series of results by N. Gupta.

Keywords

group theory finite groups finite group theory

Cite

@article{arxiv.1803.09428,
  title  = {An odd order group without the dimension property},
  author = {Laurent Bartholdi and Roman Mikhailov},
  journal= {arXiv preprint arXiv:1803.09428},
  year   = {2021}
}

Comments

This article has been superseded by arXiv:1805.10894

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