An odd order group without the dimension property

Laurent Bartholdi; Roman Mikhailov

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arXiv · 1803.09428

An odd order group without the dimension property

Laurent Bartholdi·Roman Mikhailov

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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.

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Laurent Bartholdi, Roman Mikhailov. 2018-03-26. An odd order group without the dimension property. https://arxiv.org/abs/1803.09428

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