Regular Covering of $S^1 vee S^1$ with genus 1
$begingroup$
The question is to prove that every finitely generated free group can be realized as a normal subgroup of the free group F(2). I want to do it by considering regular covers of $S^1lor S^1$. For the normal free subgroups with more than 2 generators, they correspond to the regular $n$-gons as following:
My problem is for the simplest case-- what is the regular covering corresponding to a cyclic normal subgroup of F(2)? Does such subgroup exist? Thank you!
covering-spaces free-groups
edited Dec 5 '18 at 3:32
Andrews
3831317
asked Dec 5 '18 at 2:52
user392347user392347
255
$endgroup$
add a comment |
$begingroup$
The question is to prove that every finitely generated free group can be realized as a normal subgroup of the free group F(2). I want to do it by considering regular covers of $S^1lor S^1$. For the normal free subgroups with more than 2 generators, they correspond to the regular $n$-gons as following:
My problem is for the simplest case-- what is the regular covering corresponding to a cyclic normal subgroup of F(2)? Does such subgroup exist? Thank you!
covering-spaces free-groups
edited Dec 5 '18 at 3:32
Andrews
3831317
asked Dec 5 '18 at 2:52
user392347user392347
255
$endgroup$
add a comment |
$begingroup$
The question is to prove that every finitely generated free group can be realized as a normal subgroup of the free group F(2). I want to do it by considering regular covers of $S^1lor S^1$. For the normal free subgroups with more than 2 generators, they correspond to the regular $n$-gons as following:
My problem is for the simplest case-- what is the regular covering corresponding to a cyclic normal subgroup of F(2)? Does such subgroup exist? Thank you!
covering-spaces free-groups
edited Dec 5 '18 at 3:32
Andrews
3831317
asked Dec 5 '18 at 2:52
user392347user392347
255
$endgroup$
The question is to prove that every finitely generated free group can be realized as a normal subgroup of the free group F(2). I want to do it by considering regular covers of $S^1lor S^1$. For the normal free subgroups with more than 2 generators, they correspond to the regular $n$-gons as following:
My problem is for the simplest case-- what is the regular covering corresponding to a cyclic normal subgroup of F(2)? Does such subgroup exist? Thank you!
covering-spaces free-groups
covering-spaces free-groups
edited Dec 5 '18 at 3:32
Andrews
3831317
asked Dec 5 '18 at 2:52
user392347user392347
255
edited Dec 5 '18 at 3:32
Andrews
3831317
asked Dec 5 '18 at 2:52
user392347user392347
255
edited Dec 5 '18 at 3:32
Andrews
3831317
edited Dec 5 '18 at 3:32
Andrews
3831317
edited Dec 5 '18 at 3:32
Andrews
3831317
3831317
asked Dec 5 '18 at 2:52
user392347user392347
255
asked Dec 5 '18 at 2:52
user392347user392347
255
asked Dec 5 '18 at 2:52
user392347user392347
255
255
add a comment |
add a comment |
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