Group theory and generalizations Infinite groups and combinatorial group theory Concept
One-relator group
Summary
A one-relator group is a group with a presentation that has a single defining relator. Examples are , the fundamental groups of closed surfaces, and the Baumslag–Solitar groups. They are the natural next class after free groups, and they have a rich general theory. Magnus proved the Freiheitssatz for them and showed that their word problem is solvable.
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| Tag | 68AFPHR4GN |
|---|---|
| URI | m2://68AFPHR4GN |
| Kind | concept |
| Writing | W0 stub |
| MSC | 20F05, 20F06 |
| Specializes | Group |
| Same as | |
| Changed | 2 November 2026 |
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