Abstract
It is proved that a torsion-free group\(\mathfrak{G}\), in which every infinite proper subgroup is distinct from its normalizer satisfies the normalizer condition, i.e., every proper subgroup is distinct from its normalizer.
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S. N. Chernikov, “Infinite groups with some given properties of its systems of infinite subgroups,” Dokl. Akad. Nauk SSSR,159, No. 4, 759–760 (1964).
S. N. Chernikov, “Groups with given properties of systems of infinite subgroups,” Dokl. Akad. Nauk SSSR,171, No. 4, 806–809 (1966).
B. I. Plotkin, “On the theory of locally nilpotent groups,” Dokl. Akad. Nauk SSSR,76, 639–641 (1951).
M. Hall, Theory of Groups [Russian translation], Moscow (1962).
S. N. Chernikov, “Infinite special groups,” Matem. sb.,6, No. 2, 199–214 (1939).
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Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 45–50, January, 1968.
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Chernikov, S.N. On the normalizer condition. Mathematical Notes of the Academy of Sciences of the USSR 3, 28–30 (1968). https://doi.org/10.1007/BF01386961
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DOI: https://doi.org/10.1007/BF01386961