Polycyclic groups with automorphisms of order four

Xu, Tao, Zhou, Fang, and Liu, Heguo. "Polycyclic groups with automorphisms of order four." Czechoslovak Mathematical Journal 66.2 (2016): 575-582. <http://eudml.org/doc/280100>.

@article{Xu2016,
abstract = {In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if $\alpha $ is an automorphism of order four of a polycyclic group $G$ and the map $\varphi \colon G\rightarrow G$ defined by $g^\{\varphi \}=[g,\alpha ]$ is surjective, then $G$ contains a characteristic subgroup $H$ of finite index such that the second derived subgroup $H^\{\prime \prime \}$ is included in the centre of $H$ and $C_\{H\}(\alpha ^\{2\})$ is abelian, both $C_\{G\}(\alpha ^\{2\})$ and $G/[G,\alpha ^\{2\}]$ are abelian-by-finite. These results extend recent and classical results in the literature.},
author = {Xu, Tao, Zhou, Fang, Liu, Heguo},
journal = {Czechoslovak Mathematical Journal},
keywords = {polycyclic group; regular automorphism; surjectivity},
language = {eng},
number = {2},
pages = {575-582},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Polycyclic groups with automorphisms of order four},
url = {http://eudml.org/doc/280100},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Xu, Tao
AU - Zhou, Fang
AU - Liu, Heguo
TI - Polycyclic groups with automorphisms of order four
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 575
EP - 582
AB - In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if $\alpha $ is an automorphism of order four of a polycyclic group $G$ and the map $\varphi \colon G\rightarrow G$ defined by $g^{\varphi }=[g,\alpha ]$ is surjective, then $G$ contains a characteristic subgroup $H$ of finite index such that the second derived subgroup $H^{\prime \prime }$ is included in the centre of $H$ and $C_{H}(\alpha ^{2})$ is abelian, both $C_{G}(\alpha ^{2})$ and $G/[G,\alpha ^{2}]$ are abelian-by-finite. These results extend recent and classical results in the literature.
LA - eng
KW - polycyclic group; regular automorphism; surjectivity
UR - http://eudml.org/doc/280100
ER -