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On a Property of Nilpotent Groups

Published online by Cambridge University Press:  20 November 2018

Michael Dokuchaev
Michael Dokuchaev*
Affiliation:
Uzhgorod State University, Uzhgorod 294000, Ukraine
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Abstract

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Let g be an element of a group G and [g, G] = 〈g-1a-1ga | a ∊ G〉. We prove that if G is locally nilpotent then for each g,t ∊ G either g[g, G] = t[t, G] or g[g, G] ∩ t[t, G] = Ø. The converse is true if G is finite.

Keywords

20D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 174 - 177
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Dokuchaev, M. A., Torsion units in integral group rings of nilpotent metabelian groups, Commun. Algebra (2) 20(1992), 423–435.Google Scholar
2. Gorenstein, D., Finite groups, Harper and Row, New York, 1968.Google Scholar
3. Kurosh, A. G., The theory of groups, II, Chelsea Publ. Co., New York, 1956.Google Scholar
4. Sehgal, S. K., Topics in group rings, Marcel Dekker, New York, 1978.Google Scholar