We consider the orientation-preserving actions of finite groups G on pairs (S3,), where is a connected graph of genus g > 1, embedded in S3. For each g we give the maximum order mg of such G acting on (S3,) for all such ⊂ S3. Indeed we will classify all graphs ⊂ S3 which realize these mg in different levels: as abstract graphs and as spatial graphs, as well as their group actions. Such maximum orders without the condition “orientation-preserving” are also addressed.

EB00000003426K

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