Difference between revisions
burnside-problem
Status and infobox
- status:
—→ refuted - tier:
—→ V3 - kind:
—→ problem - year:
—→ 1902 - statement:
—→ Is a finitely generated group in which every element has finite order necessarily finite?
Source +21 −0
+---
+title: Burnside problem
+kind: problem
+status: refuted
+tier: V3
+year: 1902
+authors: William Burnside
+statement: Is a finitely generated group in which every element has finite order necessarily finite?
+space: algebra
+---
+No: infinite such groups exist, even with a uniform bound on the orders. The restricted version, which asks only about finite quotients, is true, and Efim Zelmanov's proof of it won a Fields Medal in 1994.
+
+*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*
+
+Posed 1902, William Burnside. Closed 1964 Golod–Shafarevich (general); 1968 Novikov–Adian (bounded exponent); restricted version solved by Zelmanov, 1991.
+
+## Sources
+
+- [Wikipedia: Burnside problem](https://en.wikipedia.org/wiki/Burnside_problem)
+
+[[Space:algebra|Algebra and groups]] · [[Continent:mathematics|Mathematics]]
Revision 54 as rendered
No: infinite such groups exist, even with a uniform bound on the orders. The restricted version, which asks only about finite quotients, is true, and Efim Zelmanov's proof of it won a Fields Medal in 1994.
Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.
Posed 1902, William Burnside. Closed 1964 Golod–Shafarevich (general); 1968 Novikov–Adian (bounded exponent); restricted version solved by Zelmanov, 1991.