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. 
@article{VSGU_2022_28_3-4_a1,
     author = {G. V. Voskresenskaya},
     title = {On group characterization by numbers of conjugate classes},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {18--25},
     publisher = {mathdoc},
     volume = {28},
     number = {3-4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2022_28_3-4_a1/}
}
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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/