Geodesic
On group characterization by numbers of conjugate classes
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 28 (2022) no. 3-4, pp. 18-25

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Let $c(n,G)$ be a number of conjugate elements of order n in a group $G.$ In the article we study the problem of recognition of finite group by the set $\mathrm{ncl}(G)$ that consists of numbers $c(n,G).$ We prove that Abelian groups can be recognized by the set $\mathrm{ncl}(G)$ when the order of the group is known. We also describe some other types of groups that can be recognized. The examples of non-isomorphic groups with the same sets $\mathrm{ncl}(G)$ are given. Some theorems about a group recognition by partial conditions on $c(n,G)$ are proved.
Keywords: finite group, class of conjugate elements, order of element, genetic code, Sylow theorem, Abelian group, alternating group, dihedral groups. 
G. V. Voskresenskaya. On group characterization by numbers of conjugate classes. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 28 (2022) no. 3-4, pp. 18-25. http://geodesic.mathdoc.fr/item/VSGU_2022_28_3-4_a1/
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     title = {On group characterization by numbers of conjugate classes},
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