19.11 (2018)

Editors’ comment of 2021: It is proved that every group $G$ contains at least $\varepsilon \log |G|/(\log \log |G|)^8$ conjugacy classes for some fixed $\varepsilon > 0$ (L. Pyber, J. London Math. Soc. (2), 46, no. 2 (1992), 239–249). It is also proved that for every $\varepsilon > 0$ there exists $\delta > 0$ such that every finite group $G$ of order at least 3 has at least $\delta \log_2 |G|/(\log_2 \log_2 |G|)^{3+\varepsilon}$ conjugacy classes (B. Baumeister, A. Maróti, H. P. Tong Viet, Forum Math., 29, no. 2 (2017), 259–275).