Timeline for Classes of groups with finitely many retracts
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2023 at 11:42 | comment | added | Dave Benson | Ah, so I'm a representation theorist. That makes sense. | |
| Jun 7, 2023 at 10:59 | comment | added | YCor | @DaveBenson extension of A by B means kernel A, quotient B, or kernel B, quotient A, according to different communities. In geometric group theory the first convention is the most usual, while in representation theory the second convention is the most usual, as far as I could observe. | |
| Jun 7, 2023 at 6:50 | review | Close votes | |||
| Jun 12, 2023 at 3:05 | |||||
| Jun 7, 2023 at 5:24 | history | edited | M.Ramana | CC BY-SA 4.0 |
added 189 characters in body
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| Jun 6, 2023 at 20:28 | comment | added | Dave Benson | @DerekHolt Fair enough. | |
| Jun 6, 2023 at 20:07 | comment | added | Derek Holt | @DaveBenson In my experience "extension of group $X$ by group $Y$" is used about equally often with both meanings, so there is no usual meaning. In any case the "Recall that ..." sentence in the post deos not resolve the possible confusion. | |
| Jun 6, 2023 at 19:40 | comment | added | Dave Benson | The usual usage is that a group is X-by-Y if it has a normal subgroup in class X with quotient in class Y. This is also the usual meaning of an extension of a group in class Y by a group in class X, NOT of one in class X by one in class Y. So which do you mean? | |
| Jun 6, 2023 at 17:23 | comment | added | YCor | And more generally, indecomposable abelian groups (this includes all subgroups of $\mathbf{Q}$, but larger ones, including "most" subgroups of $\mathbf{Q}^n$, and also, for an uncountable example, the group of $p$-adics). | |
| Jun 6, 2023 at 17:17 | comment | added | Emil Jeřábek | Prüfer $p$-groups are another example | |
| Jun 6, 2023 at 17:07 | comment | added | YCor | I was going to mention simple groups as a trivial example. | |
| Jun 6, 2023 at 16:54 | answer | added | Jeremy Rickard | timeline score: 2 | |
| Jun 6, 2023 at 14:37 | history | asked | M.Ramana | CC BY-SA 4.0 |