Fusion systems on a Sylow 3-subgroup of the McLaughlin group

Author:

Baccanelli Elisa1,Franchi Clara1,Mainardis Mario2

Affiliation:

1. Dipartimento di Matematica e Fisica , Università Cattolica del Sacro Cuore , Via Musei 41, 25121 Brescia , Italy

2. Dipartimento di Scienze Matematiche, Informatiche e Fisiche X , Università di Udine , Via delle Scienze 206, 33100 Udine , Italy

Abstract

Abstract We determine all saturated fusion systems {\mathcal{F}} on a Sylow 3-subgroup of the sporadic McLaughlin group that do not contain any non-trivial normal 3-subgroup and show that they are all realizable.

Funder

Università degli Studi di Udine

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference19 articles.

1. M. Aschbacher, On the maximal subgroups of the finite classical groups, Invent. Math. 76 (1984), no. 3, 469–514.

2. M. Aschbacher, Finite Group Theory, 2nd ed., Cambridge Stud. Adv. Math. 10, Cambridge University Press, Cambridge, 2000.

3. M. Aschbacher, R. Kessar and B. Oliver, Fusion Systems in Algebra and Topology, London Math. Soc. Lecture Note Ser. 391, Cambridge University Press, Cambridge, 2011.

4. E. Baccanelli, Reduced fusion systems on Sylow 3-subgroups of the Mclaughlin group, PhD Thesis, Università di Milano Bicocca, 2017.

5. J. N. Bray, D. F. Holt and C. M. Roney-Dougal, The Maximal Subgroups of the Low-Dimensional Finite Classical Groups, London Math. Soc. Lecture Note Ser. 407, Cambridge University Press, Cambridge, 2013.

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