Volume 50, Issue 4
On Finite Groups Whose Nilpotentisers Are Nilpotent Subgroups

Seyyed Majid Jafarian Amiri & Hojjat Rostami

J. Math. Study, 50 (2017), pp. 307-313.

Published online: 2018-04

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  • 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 :hx,yiis nil potent}. 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.

  • Keywords

Finite group nilpotentiser N -group.

  • AMS Subject Headings

20D60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

sm_jafarian@znu.ac.ir (Seyyed Majid Jafarian Amiri)

h.rostami5991@gmail .com (Hojjat Rostami)

  • BibTex
  • RIS
  • TXT
@Article{JMS-50-307, author = {Amiri , Seyyed Majid Jafarian and Rostami , Hojjat}, title = {On Finite Groups Whose Nilpotentisers Are Nilpotent Subgroups}, journal = {Journal of Mathematical Study}, year = {2018}, volume = {50}, number = {4}, pages = {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 :hx,yiis nil potent}. 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n4.17.01}, url = {http://global-sci.org/intro/article_detail/jms/11319.html} }
TY - JOUR T1 - On Finite Groups Whose Nilpotentisers Are Nilpotent Subgroups AU - Amiri , Seyyed Majid Jafarian AU - Rostami , Hojjat JO - Journal of Mathematical Study VL - 4 SP - 307 EP - 313 PY - 2018 DA - 2018/04 SN - 50 DO - http://doi.org/10.4208/jms.v50n4.17.01 UR - https://global-sci.org/intro/article_detail/jms/11319.html KW - Finite group KW - nilpotentiser KW - N -group. AB -

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 :hx,yiis nil potent}. 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.

Seyyed Majid Jafarian Amiri & Hojjat Rostami. (2019). On Finite Groups Whose Nilpotentisers Are Nilpotent Subgroups. Journal of Mathematical Study. 50 (4). 307-313. doi:10.4208/jms.v50n4.17.01
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