Geodesic
On Finite Groups with Restrictions on Centralizers
Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 483-495.

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Denote by $w(n)$ the number of factors in a representation of a positive integer $n$ as a product of primes. If $H$ is a subgroup of a finite group $G$, then we set $w(H)=w(|H|)$ and $v(G)=\max \{w(C(g))\mid g\in G\setminus Z(G)\}$. In the present paper we present the complete description of groups with nontrivial center that satisfy the condition $v(G)=4$. 
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V. A. Antonov; I. A. Tyurina; A. P. Cheskidov. On Finite Groups with Restrictions on Centralizers. Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 483-495. http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a0/

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