Timeline for Applications of Tits' alternative in algebraic number theory
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 13, 2020 at 6:35 | comment | added | Sunny | I don't know how it is applicable in algebraic number theory but it is a very important result in Geometric group theory, a branch deals with the study of finitely generated infinite groups using geometry. Tit's alternative is one of the key step used in proving one of the famous theorem of Gromov's which says that a finitely generated group has polynomial growth iff it has nilpotent subgroup of finite index. | |
| Jul 13, 2020 at 0:25 | comment | added | YCor | The proof of the Tits alternative really consists, assuming that $G$ is not virtually solvable, in constructing a free subgroup (rather, say, that assuming that $G$ contains no free subgroup, that $G$ is solvable). Hence the question is maybe what such free subgroups are useful to? | |
| Jul 12, 2020 at 23:30 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title, changed tag
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| Jul 12, 2020 at 16:06 | history | edited | James Moriarty | CC BY-SA 4.0 |
edited title
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| Jul 12, 2020 at 15:33 | review | First posts | |||
| Jul 12, 2020 at 15:54 | |||||
| Jul 12, 2020 at 15:29 | history | asked | James Moriarty | CC BY-SA 4.0 |