Year: 2017
Author: Seyyed Majid Jafarian Amiri, Hojjat Rostami
Journal of Mathematical Study, Vol. 50 (2017), Iss. 4 : pp. 307–313
Abstract
Let G be a finite group and x∈G. The nilpotentiser of x in G is defined to be the subset NilG(x)={y∈G:⟨x,y⟩ is nilpotent}. G is called an N-group (n-group) if NilG(x) is a subgroup (nilpotent subgroup) of G for all x∈G∖Z∗(G) where Z∗(G) is the hypercenter of G. In the present paper, we determine finite N-groups in which the centraliser of each noncentral element is abelian. Also we classify all finite n-groups.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v50n4.17.01
Journal of Mathematical Study, Vol. 50 (2017), Iss. 4 : pp. 307–313
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 7
Keywords: Finite group nilpotentiser N-group.