Timeline for does this group have a name?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 23, 2011 at 2:42 | comment | added | Steve D | The normal closure of $c$ is infinite. | |
| Dec 3, 2010 at 3:09 | vote | accept | dan | ||
| Dec 3, 2010 at 1:38 | comment | added | Denis Osin | It is not quite clear for me why $c$ commutes with all conjugates by $b^n$. | |
| Dec 3, 2010 at 1:26 | history | edited | Denis Osin | CC BY-SA 2.5 |
added 155 characters in body
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| Dec 3, 2010 at 1:21 | comment | added | user6976 | It looks like the group is virtually cyclic. In fact it is an extension of the 4-element Klein group by the infinite cyclic group that permutes the two generating involutions. Do a change of variables $c=ba$. Get $c^2=1$, $c$ commutes with all conjugates by $b^n$. So the group is a factor-group of the lamplighter group. Now the relation $a^2b=ba^2$ means, if I am not mistaken, $cbcb=bcbc$. Which means $cc^b=c^bc^{b^2}$ or $c=c^{b^2}$. So the normal subgroup generated by $c$ is of order 4. Right? | |
| Dec 3, 2010 at 1:15 | history | answered | Denis Osin | CC BY-SA 2.5 |