An odd order group without the dimension property

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.

arXiv commentThis article has been superseded by arXiv:1805.10894