Title : ( On groups satisfying a symmetric Engel word )
Authors: M. Farrokhi D. G , Mohammad Reza Rajabzadeh Moghaddam ,
Full TextAbstract
Abstract We show that a finite group satisfying the law [y,nx]=[x,ny][y,nx]=[x,ny] ( n>1n>1 ) is nilpotent and utilizing the results of Macdonalds on the structure of groups satisfying the law [y,x]=[x,y][y,x]=[x,y] , we investigate groups satisfying both of the laws [y,x]=[x,y][y,x]=[x,y] and [y,nx]=[x,ny][y,nx]=[x,ny] for small n. Our results can be applied to obtain special commutators, which can be expressed as the product of commutators squares.
Keywords
Symmetry · Engel word · Engel group · Nilpotent group
@article{paperid:1065650,
author = {M. Farrokhi D. G and Rajabzadeh Moghaddam, Mohammad Reza},
title = {On groups satisfying a symmetric Engel word},
journal = {Ricerche di Matematica},
year = {2016},
volume = {65},
number = {1},
month = {June},
issn = {0035-5038},
pages = {15--20},
numpages = {5},
keywords = {Symmetry · Engel word · Engel group · Nilpotent group},
}
%0 Journal Article
%T On groups satisfying a symmetric Engel word
%A M. Farrokhi D. G
%A Rajabzadeh Moghaddam, Mohammad Reza
%J Ricerche di Matematica
%@ 0035-5038
%D 2016
