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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1316–1321 (Mi smj2163)  
Locally nilpotent groups containing an element that commutes with only finitely many of its conjugates

V. E. Kislyakov

Institute of Basic Training, Siberian Federal University, Krasnoyarsk
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Abstract: We prove that a locally nilpotent group containing an element that commutes with only finitely many of its conjugates includes an abelian normal subgroup. We find some necessary conditions for the normal closure of such an element to be nilpotent.
Keywords: locally nilpotent group, nilpotent group, abelian normal subgroup, normal closure of an element in a group, element commuting with only finitely many of its conjugates.
Received: 31.05.2010
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 6, Pages 1043–1046
DOI: https://doi.org/10.1007/s11202-010-0102-8
Bibliographic databases:
Document Type: Article
UDC: 512.544
Language: Russian
Citation: V. E. Kislyakov, “Locally nilpotent groups containing an element that commutes with only finitely many of its conjugates”, Sibirsk. Mat. Zh., 51:6 (2010), 1316–1321; Siberian Math. J., 51:6 (2010), 1043–1046
Citation in format AMSBIB
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