Timeline for Does the sequence (Number of groups of even order $\le n$) / (Number of groups of order $\leq n$) converge? If not, what are its cluster points?
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2020 at 23:53 | vote | accept | The Thin Whistler | ||
| Nov 22, 2020 at 9:44 | comment | added | Emil Jeřábek | Also related: mathoverflow.net/questions/150603/… | |
| Nov 21, 2020 at 22:28 | answer | added | Qiaochu Yuan | timeline score: 4 | |
| Nov 21, 2020 at 22:20 | comment | added | The Thin Whistler | @Carl-FredrikNybergBrodda WHOOOOOOOOOOOOOW, that just blew my mind! | |
| Nov 21, 2020 at 22:09 | comment | added | Carl-Fredrik Nyberg Brodda | Re: almost all groups are 2-groups, you might find this old StackExchange answer interesting. | |
| Nov 21, 2020 at 22:02 | comment | added | Derek Holt | If you do a search for "almost all groups are 2-groups" you will get plenty of hits and information on known results. | |
| Nov 21, 2020 at 21:59 | comment | added | The Thin Whistler | @DerekHolt: Whow, that is interesting! Any References? | |
| Nov 21, 2020 at 21:55 | comment | added | Derek Holt | There are even stronger conjectures that almost all finite groups are $2$-groups $G$ of nilpotency class $2$ in which $Z(G)=[G,G]$ and $G/Z(G)$ and $Z(G)$ are both elementary abelian. The known lower bounds are derived from counting groups of this type. | |
| Nov 21, 2020 at 21:52 | comment | added | Derek Holt | There is widespread belief among specialists in the area that almost all finite groups (meaning isomorphism classes) have order a power of two, but it remains unproven, and the current techniques do not appear to be strong enough to prove it. So that would imply that the if we let $t_n$ be the number of isomorphism classes of groups of order a power of two less than $n$ divided by the number of all groups od order less than $n$, then $t_n \to 1$ as $n \to \infty$. | |
| Nov 21, 2020 at 21:46 | comment | added | The Thin Whistler | That is true, but I think counting isomorphy classes is what my student was after. | |
| Nov 21, 2020 at 21:45 | comment | added | YCor | Note that counting over isomorphy classes is one way of counting groups. It could be also a random law over $n$ elements, or a random subgroup of the symmetric group, etc. | |
| Nov 21, 2020 at 21:43 | history | edited | The Thin Whistler | CC BY-SA 4.0 |
deleted 60 characters in body
|
| Nov 21, 2020 at 21:42 | comment | added | The Thin Whistler | @YCor that is true | |
| Nov 21, 2020 at 21:41 | comment | added | YCor | "$\#$ Number of" sounds redundant, since $\#$ means "number of", so it sounds like "number of number of". | |
| Nov 21, 2020 at 21:39 | history | edited | YCor | CC BY-SA 4.0 |
formatting
|
| Nov 21, 2020 at 21:39 | history | edited | The Thin Whistler | CC BY-SA 4.0 |
added 416 characters in body
|
| Nov 21, 2020 at 21:34 | history | asked | The Thin Whistler | CC BY-SA 4.0 |