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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

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4. Sehgal, S. K., Topics in group rings, Marcel Dekker, New York, 1978.Google Scholar