Permutability of centre-by-finite groups

Piochi, Brunetto. "Permutability of centre-by-finite groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 83.1 (1989): 153-158. <http://eudml.org/doc/287513>.

@article{Piochi1989,
abstract = {Let $G$ be a group and $m$ be an integer greater than or equal to $2$. $G$ is said to be $m$-permutable if every product of $m$ elements can be reordered at least in one way. We prove that, if $G$ has a centre of finite index $z$, then $G$ is $(1 + [z/2])$-permutable. More bounds are given on the least $m$ such that $G$ is $m$-permutable.},
author = {Piochi, Brunetto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Centre-by-Finite Groups; Rewritable groups; Permutability; permutation property; rewritable groups; permutable groups; finite-by- Abelian-by-finite groups; center; finite index},
language = {eng},
month = {12},
number = {1},
pages = {153-158},
publisher = {Accademia Nazionale dei Lincei},
title = {Permutability of centre-by-finite groups},
url = {http://eudml.org/doc/287513},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Piochi, Brunetto
TI - Permutability of centre-by-finite groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 153
EP - 158
AB - Let $G$ be a group and $m$ be an integer greater than or equal to $2$. $G$ is said to be $m$-permutable if every product of $m$ elements can be reordered at least in one way. We prove that, if $G$ has a centre of finite index $z$, then $G$ is $(1 + [z/2])$-permutable. More bounds are given on the least $m$ such that $G$ is $m$-permutable.
LA - eng
KW - Centre-by-Finite Groups; Rewritable groups; Permutability; permutation property; rewritable groups; permutable groups; finite-by- Abelian-by-finite groups; center; finite index
UR - http://eudml.org/doc/287513
ER -