Timeline for Finitely presented group in which every element is conjugate to its square
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| May 9, 2014 at 19:09 | comment | added | YCor | 2) As long as the question concerns finitely presented groups, it is not true that one is led to the simple case (because any nontrivial fg group has a simple quotient, but for a finitely presented group, one does not necessarily get a finitely presented simple quotient); actually Miller's group (an infinite f.p. group all of whose nontrivial quotients have a nonsolvable word problem) has no finitely presented simple quotient at all. | |
| May 9, 2014 at 19:07 | comment | added | YCor | 1) This Higman group doesn't work: it has an action on a tree with hyperbolic elements. Such a hyperbolic element $g$ cannot be conjugate to their square, because if $L$ is its displacement length then the displacement of $g^2$ is $2L$, whence $L=0$. | |
| May 9, 2014 at 16:49 | review | First posts | |||
| May 9, 2014 at 16:49 | |||||
| May 9, 2014 at 16:32 | history | answered | Eric Moorhouse | CC BY-SA 3.0 |