Geodesic
A Sufficient Condition for Solvability in Groups Admitting Elementary Abelian Operator Groups
Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 848-855

Voir la notice de l'article provenant de la source Cambridge University Press

Generalizing a celebrated theorem of Thompson, R. P. Martineau has established [4; 5] that a finite group which admits an elementary abelian group of automorphisms with trivial fixed-point subgroup is necessarily solvable. A critical observation in his approach to this problem is the fact that, corresponding to each prime divisor of its order, such a group contains a unique Sylow subgroup invariant (as a set) under the action. Hence, the theorem we shall derive here represents a modest extension of Martineau's result. 
Pettet, Martin R. A Sufficient Condition for Solvability in Groups Admitting Elementary Abelian Operator Groups. Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 848-855. doi: 10.4153/CJM-1977-087-x
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