Timeline for An endomorphism of free groups

9 events

when toggle format	what		by	license	comment
Sep 26, 2017 at 20:48	answer	added	Andrew Clifford		timeline score: 1
Sep 25, 2017 at 13:26	vote	accept	Stevie H
Sep 25, 2017 at 8:41	comment	added	Aurel		@DerekHolt Indeed, I messed up my actions, thanks. What I meant was that $(1,2)(1,2,3,4)$ sends $1\mapsto 1$ and $2\mapsto 3$ and therefore conjugates $(1,2)$ to $(1,3)$ for a suitable normalisation of conjugation.
Sep 25, 2017 at 8:04	comment	added	Derek Holt		@aurel $g_1=\alpha_1\alpha_2$ gives the same result as $g_1=\alpha_2$. I think you mean $g_1= \alpha_2\alpha_1$. Also, if you are suing right actions, then $(1,2)^{(1,2)(1,2,3,4)} = (1,2)^{(1,2,3,4)}=(2,3)$.
Sep 25, 2017 at 8:00	answer	added	YCor		timeline score: 16
Sep 25, 2017 at 7:24	comment	added	Aurel		@Seirios It is not clear to me. In fact, $S_4$ is generated by $(1,2)$ and $(1,2,3,4)$ but not by $(1,3) = (1,2)^{(1,2)(1,2,3,4)}$ and $(1,2,3,4)$, so in $F_2 = \langle\alpha_1,\alpha_2\rangle$, the endomorphism $\psi$ given by $g_1 = \alpha_1\alpha_2$ and $g_2 = 1$ is not an automorphism.
Sep 25, 2017 at 5:37	review	Close votes
Sep 25, 2017 at 11:32
Sep 25, 2017 at 4:56	review	First posts
Sep 25, 2017 at 5:50
Sep 25, 2017 at 4:54	history	asked	Stevie H	CC BY-SA 3.0