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Tr. Mat. Inst. Steklova, 2016, Volume 292, Pages 149–158 (Mi tm3698)  

Frattini and related subgroups of mapping class groups

G. Masbauma, A. W. Reidb

a Institut de Mathématiques de Jussieu–PRG (UMR 7586 du CNRS), Equipe Topologie et Géométrie Algébriques, Case 247, 4 pl. Jussieu, 75252 Paris Cedex 5, France
b Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA

Abstract: 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 $\Phi _f(G)$ is nilpotent when $G$ is a finitely generated subgroup of $\Gamma _{g,b}$, in this paper we compute $\Phi _f(G)$ for certain subgroups of $\Gamma _{g,b}$. In particular, we answer Ivanov's question in the affirmative for these subgroups of $\Gamma _{g,b}$.

Funding Agency Grant Number
National Science Foundation
This work was partially supported by the NSF.


DOI: https://doi.org/10.1134/S037196851601009X

Full text: PDF file (209 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 292, 143–152

Bibliographic databases:

UDC: 512.54+515.1
Received: December 9, 2014
Language:

Citation: G. Masbaum, A. W. Reid, “Frattini and related subgroups of mapping class groups”, Algebra, geometry, and number theory, Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday, Tr. Mat. Inst. Steklova, 292, MAIK Nauka/Interperiodica, Moscow, 2016, 149–158; Proc. Steklov Inst. Math., 292 (2016), 143–152

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\publ MAIK Nauka/Interperiodica
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