## Advanced Studies in Pure Mathematics

### 2F-modules with quadratic offender for the finite simple groups

Gernot Stroth

#### Abstract

There is a long running project due to U. Meierfrankenfeld and the author to investigate the so called small modules for the finite simple groups. These modules show up in the amalgam method which recently became important for the revision of parts of the classification of the finite simple groups. A small module either is a quadratic module or a module on which an elementary abelian group acts such that the codimension of the centralizer is small compared with its order. In this paper we determine all irreducible modules $V$ over $GF(2)$ for the finite simple groups $G$ such that $|V : C_V(A)| \le |A|^2$ for some nontrivial elementary abelian subgroup $A$ of $G$ where in addition we have $[V, A, A] = 1$.

#### Article information

Dates
Revised: 26 January 2001
First available in Project Euclid: 29 December 2018

https://projecteuclid.org/ euclid.aspm/1546124714

Digital Object Identifier
doi:10.2969/aspm/03210391

Mathematical Reviews number (MathSciNet)
MR1893506

Zentralblatt MATH identifier
1008.20004

#### Citation

Stroth, Gernot. 2F-modules with quadratic offender for the finite simple groups. Groups and Combinatorics: In memory of Michio Suzuki, 391--400, Mathematical Society of Japan, Tokyo, Japan, 2001. doi:10.2969/aspm/03210391. https://projecteuclid.org/euclid.aspm/1546124714