Frattini and related subgroups of Mapping Class Groups
Let $\Gamma_{g,b}$ denote the orientation-preserving Mapping Class Group of a closed orientable surface of genus $g$ with $b$ punctures. For a group $G$ let $\Phi_f(G)$ denote the intersection of all maximal subgroups of finite index in $G$. Motivated by a question of Ivanov as to whether $\Phi_f(G)...
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