Geodesic
Groups with Small Centralizers
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 643-655.

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Denote by $w(n)$ the number of factors in the representation of a positive integer $n$ in the form of a product of primes. For a subgroup $>H$ of a finite group $G$, we set $w(H)=w(|H|)$ and $v(G)=\max\{w(C(g))\mid g\in G\setminus Z(G)\}$. In the present paper, the complete description of centerfree groups satisfying the condition $v(G)= 4$ is presented. 
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V. A. Antonov; I. A. Tyurina; A. P. Cheskidov. Groups with Small Centralizers. Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 643-655. http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a0/

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