Geodesic
On groups with a finite number of automorphisms
Sbornik. Mathematics, Tome 15 (1971) no. 4, pp. 568-575 
V. T. Nagrebetskii. On groups with a finite number of automorphisms. Sbornik. Mathematics, Tome 15 (1971) no. 4, pp. 568-575. http://geodesic.mathdoc.fr/item/SM_1971_15_4_a5/
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     title = {On groups with a~finite number of automorphisms},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that in groups having only a finite number of automorphisms the set of all prime numbers dividing the finite orders of elements is finite. The dependence of the order of a finite group on the number of its automorphisms is obtained. A new proof is given of the well-known result of Baer that a periodic group with a finite number of automorphisms is finite. It is proved that a group with a finite number of monomorphisms is finite. The final result generalizes the well-known theorem of Baer that a group with a finite number of endomorphisms is finite. Bibliography: 5 titles.

[1] A. G. Kurosh, Teoriya grupp, Nauka, Moskva, 1967 | MR | Zbl

[2] R. baer, “Representations of groups as quotient groups. II. Minimal central chains of a group”, Trans. Amer. Math. Soc., 58:3 (1945), 348–389 | DOI | MR | Zbl

[3] J. L. Alperin, “Groups with finitelly many automorphisms”, Pacific J. Math., 12:1 (1962), 1–5 | MR | Zbl

[4] R. Baer, “Finite extensions of abelian groups with minimum condition”, Trans. Amer. Math. Soc., 79 (1955), 521–540 | DOI | MR | Zbl

[5] V. T. Nagrebetskii, “O chisle konechnykh grupp s zadannoi gruppoi avtomorfizmov”, Matem. sb., 83(125) (1970), 524–526