Geodesic
Finite Groups with Large Irreducible Character
Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 237-246.

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In the general case, the order of a finite nonidentity group $G$ is substantially larger than the squared degree of every irreducible character $\Theta$ of $G$, i.e., $\Theta(1)^2|G|$. In the present paper, we study finite groups with an irreducible character $\Theta$ such that $$ |G|\le 2\Theta(1)^2. $$
Keywords: finite group, irreducible character, Sylow subgroup, Clifford theory, Fitting subgroup.
Mots-clés : Frobenius group, constituent, Galois group 
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L. S. Kazarin; S. S. Poiseeva. Finite Groups with Large Irreducible Character. Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 237-246. http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a8/

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