## Illinois Journal of Mathematics

### Embedding of groups and quadratic equations over groups

#### Abstract

We prove that, for every integer $n\ge2$, a finite or infinite countable group $G$ can be embedded into a 2-generated group $H$ in such a way that the solvability of quadratic equations of length at most $n$ is preserved, that is, every quadratic equation over $G$ of length at most $n$ has a solution in $G$ if and only if this equation, considered as an equation over $H$, has a solution in $H$.

#### Article information

Source
Illinois J. Math., Volume 60, Number 1 (2016), 99-115.

Dates
Revised: 19 July 2016
First available in Project Euclid: 21 June 2017