Some finiteness conditions for automorphism groups
Glasgow mathematical journal, Tome 29 (1987) no. 2, pp. 259-265

Voir la notice de l'article provenant de la source Cambridge University Press

Many authors have investigated the behaviour of the elements of finite order of a group G when finiteness conditions are imposed on the automorphism group Aut G of G. The first result was obtained in 1955 by Baer [1], who proved thata torsion group with finitely many automorphisms is finite. This theorem was generalized by Nagrebeckii in [6], where he proved that if the automorphism group Aut G is finite then the set of elements of finite order of G is a finite subgroup.
Franciosi, Silvana; Giovanni, Francesco de. Some finiteness conditions for automorphism groups. Glasgow mathematical journal, Tome 29 (1987) no. 2, pp. 259-265. doi: 10.1017/S0017089500006911
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[1] 1. Baer, R., Finite extensions of abelian groups with minimum condition, Trans. Amer. Math. Soc. 79 (1955), 521–540. Google Scholar | DOI

[2] 2. Dieudonné, J., Les determinants sur un corps non commutatif, Bull. Soc. Math. France 71 (1943), 27–45. Google Scholar | DOI

[3] 3. Franciosi, S. and de Giovanni, F., A note on groups with countable automorphism groups, Arch. Math. (Basel), 47 (1986), 12–16. Google Scholar | DOI

[4] 4. Franciosi, S., de Giovanni, F. and Robinson, D. J. S., On torsion in groups whose automorphism groups have finite rank, Rocky Mountain J. Math., to appear. Google Scholar

[5] 5. MacLane, S., Homology (Springer, 1975). Google Scholar

[6] 6. Nagrebeckiĭ, V. T., On the periodic part of a group with a finite number of automorphisms, Dokl. Akad. Nauk SSSR 205 (1972), 519–521 = Soviet Math. Dokl. 13 (1972), 953–956. Google Scholar

[7] 7. Robinson, D. J. S., Finiteness conditions and generalized soluble groups (Springer, 1972). Google Scholar | DOI

[8] 8. Robinson, D. J. S., On the cohomology of soluble groups with finite rank, J. Pure Appl. Algebra 6 (1975), 155–164. Google Scholar | DOI

[9] 9. Robinson, D. J. S., Homology of group extensions with divisible abelian kernel, J. Pure Appl. Algebra 14 (1979), 145–165. Google Scholar | DOI

[10] 10. Robinson, D. J. S., Infinite torsion groups as automorphism groups, Quart. J. Math. Oxford Ser. (2) 30 (1979), 351–364. Google Scholar | DOI

[11] 11. Rosenberg, A., The structure of the infinite general linear group, Ann. of Math. 68 (1958), 278–294. Google Scholar | DOI

[12] 12. Silcock, H. L., Metanilpotent groups satisfying the minimal condition for normal subgroups, Math. Z. 135 (1974), 165–173. Google Scholar | DOI

[13] 13. Stammbach, U., Homology in Group Theory (Lecture Notes in Mathematics 359, Springer, 1973). Google Scholar | DOI

[14] 14. Zimmerman, J., Countable torsion FC-groups as automorphism groups, Arch. Math. (Basel) 43 (1984), 108–116. Google Scholar | DOI

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