On maximal embeddings of finite quasisimple groups

Gerhard Hiss

On maximal embeddings of finite quasisimple groups

Group Theory 2020-07-10 v2

Authors: Gerhard Hiss

Abstract

If a finite quasisimple group G with simple quotient S is embedded into a suitable classical group X through the smallest degree of a projective representation of S, then the normalizer of G in X is a maximal subgroup of X, up to two series of exceptions where S is a Ree group, and four exceptions where S is sporadic.

Keywords

finite quasisimple groups maximal subgroups embeddings classical groups projective representations

Cite

@article{arxiv.1910.14300,
  title  = {On maximal embeddings of finite quasisimple groups},
  author = {Gerhard Hiss},
  journal= {arXiv preprint arXiv:1910.14300},
  year   = {2020}
}

Comments

Corrected the omission of the two series of exceptions involving the Ree groups; added a remark on the maximality of the intermediate subgroups in the exceptional cases

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