The Andrews-Curtis problem for \(\mathcal F (\mathfrak M)\) (Q1814014)
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scientific article; zbMATH DE number 5598
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Andrews-Curtis problem for \(\mathcal F (\mathfrak M)\) |
scientific article; zbMATH DE number 5598 |
Statements
The Andrews-Curtis problem for \(\mathcal F (\mathfrak M)\) (English)
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25 June 1992
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The following theorem is proved. Let \(F\) be a free group with basis \(\{x_ 1,\dots,x_ n\}\) \((n\geq 2)\), let \(H\) be a normal subgroup of \(F\) contained in the commutator subgroup \(F'\) and let \(U\) be a normal subgroup of \(F\) contained in \(H\) and containing the verbal subgroup \(V(H)\). If the group \(T\) of extended Nielsen transformations acts transitively on \(F/H\), then \(T\) acts transitively also on \(F/U\). Some consequences for the solution of the Andrews-Curtis problem in a variety are given.
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free group
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commutator subgroup
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normal subgroup
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verbal subgroup
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extended Nielsen transformations
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Andrews-Curtis problem
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variety
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