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In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven:

Theorem. The quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomorfic homeomorphic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2).

The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).
show/hide this revision's text 2 added 18 characters in body

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proventhat the :

Theorem. The quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomerfic homeomorfic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2).

The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).
show/hide this revision's text 1

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven that the quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomerfic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2). The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).