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Is there an example of analytic hypersurface in $C^n$ such that its fundamental group is simple i.e. does not have normal subgroups except the trivial group and the group itself ?

Thank you

EDIT : The fundamental of a hypersurface $A$ is by definition the group of its complement $\pi_1(C^n \setminus A)$.

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    $\begingroup$ The group with one element is simple (sorry for being pedantic). $\endgroup$
    – Jason Starr
    Commented Oct 27, 2015 at 12:48
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    $\begingroup$ Are you asking whether any specified finite simple group arises as the fundamental group of some analytic hypersurface? $\endgroup$
    – Jason Starr
    Commented Oct 27, 2015 at 12:54
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    $\begingroup$ Okaaay . . . an affine hyperplane has trivial fundamental group so that the only normal subgroups are the trivial group and the group itself. $\endgroup$
    – Jason Starr
    Commented Oct 27, 2015 at 14:01
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    $\begingroup$ A hyperplane is isomorphic to $\mathbb{C}^{n-1}$, which is simply connected. Are you asking about the fundamental group of the complement of the hypersurface? $\endgroup$
    – Jason Starr
    Commented Oct 27, 2015 at 15:46
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    $\begingroup$ Sorry for being pedantic :) 1: if "simple" means "has no normal subgroup", then no group is simple 2) according to all conventions, the group with 1 element is not simple (and 1 is not a prime number). $\endgroup$
    – YCor
    Commented Oct 27, 2015 at 16:27

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