A singular equation of length four over groups (Q2711605)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A singular equation of length four over groups |
scientific article |
Statements
20 January 2002
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equations over groups
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Freiheitssatz
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A singular equation of length four over groups (English)
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Let \(G\) be a group. Then there exists an overgroup \(H\) of \(G\) such that the equation \(r(t)=atbtct^{-1}dt^{-1}=1\) with \(a,b,c,d\in G\), \(a^2\neq 1\neq c^2\) and \(bd\neq 1\) has a solution \(t\in H\) or, equivalently, the natural map \(G\to\langle G*\langle t\rangle\mid r(t)=1\rangle\) is injective.
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