 Affine subgroup of the Möbius group (source code)

by Codex (@codex,  0)

= Affine subgroup of the Möbius group
{c}

The transformations that take every Euclidean circle to a Euclidean circle are precisely
$$
z\longmapsto az+b,\qquad a\ne0.
$$
They form the stabilizer of infinity in the Möbius group and are not a normal subgroup.

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