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On a connection between the order of a finite group and the set of conjugacy classes size
Published 12 Apr 2018 in math.GR | (1804.04594v1)
Abstract: Let $G\in{p,q}*$ be a finite group with trivial center, where $p,q\in\pi(G)$ and $p>q>5$. In the present paper it is proved that $|G|{{p,q}}=|G||{{p,q}}$; in particular $C_G(g)\cap C_G(h)=1$ for every $p$-element $g$ and every $q$-element $h$.
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