Timeline for How many finitely-generated-by-elements-of-finite-order-groups are there?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2021 at 6:59 | history | edited | JP McCarthy | CC BY-SA 4.0 |
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| Apr 16, 2021 at 11:48 | answer | added | IJL | timeline score: 6 | |
| Apr 16, 2021 at 7:33 | history | became hot network question | |||
| Apr 16, 2021 at 6:36 | comment | added | YCor | @AndyPutman yes: every virtually (free non-abelian) group is SQ-universal. In particular this applies to $\mathrm{PSL}_2(\mathbf{Z})=\langle s,t\mid s^2=t^3=1\rangle$. It's even easier to directly show the latter has continuum many normal subgroups (given that the isomorphism relation between quotients of a given finitely generated group has countable casses, it implies continuum many isomorphism classes). | |
| Apr 16, 2021 at 3:41 | vote | accept | JP McCarthy | ||
| Apr 16, 2021 at 1:31 | answer | added | Benjamin Steinberg | timeline score: 18 | |
| Apr 16, 2021 at 0:55 | comment | added | Benjamin Steinberg | Grigorchuk constructed uncountably many groups of intermediate Growth generated by 3 involutions that I believe form uncountably many isomorphism classes but I have to double check | |
| Apr 16, 2021 at 0:12 | comment | added | Gerry Myerson | Is it possible to compute the cardinality of the set of groups generated by $s,t$ with $s^2=t^3=1$? | |
| Apr 16, 2021 at 0:01 | comment | added | Andy Putman | My guess is that every f.g. group embeds into a group generated by finitely many torsion elements. Since each such group contains countably many f.g. subgroups but there are uncountably many f.g. groups, this would imply that there are uncountably many groups generated by finitely many torsion elements. | |
| Apr 15, 2021 at 23:56 | comment | added | Moishe Kohan | Most likely, continuum, for the same reason that there is continuum of finitely generated groups. | |
| Apr 15, 2021 at 23:33 | history | asked | JP McCarthy | CC BY-SA 4.0 |