Frattini and related subgroups of Mapping Class Groups
نویسندگان
چکیده
Let Γg,b denote the orientation-preserving Mapping Class Group of a closed orientable surface of genus g with b punctures. For a group G let Φf (G) denote the intersection of all maximal subgroups of finite index in G. Motivated by a question of Ivanov as to whether Φf (G) is nilpotent when G is a finitely generated subgroup of Γg,b, in this paper we compute Φf (G) for certain subgroups of Γg,b. In particular, we answer Ivanov’s question in the affirmative for these subgroups of Γg,b. 2000 MSC Classification: 20F38, 57R56
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