Timeline for When is the set of $n$-th powers in a group a subgroup?
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| Jul 18, 2019 at 16:12 | comment | added | YCor | Just to mention, existence of "many" divisible groups (e.g., algebraically closed groups) is a classical application of HNN extensions (say, this shows that every countable group embeds in a divisible countable group). More difficult, using small cancellation ideas Guba (1986) constructed finitely generated nontrivial examples, see this MO answer. To make this construction different, you maybe want to obtain non-divisible groups (and avoid trivialities such as (divisible)$\times$(abelian), e.g. imposing $\bigcap_n G^n=\{1\}$). | |
| Jul 18, 2019 at 16:02 | history | edited | Ian Agol | CC BY-SA 4.0 |
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| Jul 18, 2019 at 5:16 | history | edited | Ian Agol | CC BY-SA 4.0 |
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| Jul 17, 2019 at 21:23 | history | rollback | Ian Agol |
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| Jul 17, 2019 at 21:22 | history | edited | Ian Agol | CC BY-SA 4.0 |
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| Jul 17, 2019 at 21:08 | history | answered | Ian Agol | CC BY-SA 4.0 |