Toffalori, Carlo. "An elementary class extending abelian-by-\( G \) groups, for \( G \) infinite." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.4 (1996): 213-217. <http://eudml.org/doc/244259>.
@article{Toffalori1996,
abstract = {We show that for no infinite group \( G \) the class of abelian-by-\( G \) groups is elementary, but, at least when \( G \) is an infinite elementary abelian \( p \)-group (with \( p \) prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to \( G \) is elementary.},
author = {Toffalori, Carlo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Elementary class of structures; Abelian-by-G group; Commutator; abelian-by- group; elementary class; infinite group; elementarily equivalent; abelian group of prime exponent},
language = {eng},
month = {12},
number = {4},
pages = {213-217},
publisher = {Accademia Nazionale dei Lincei},
title = {An elementary class extending abelian-by-\( G \) groups, for \( G \) infinite},
url = {http://eudml.org/doc/244259},
volume = {7},
year = {1996},
}
TY - JOUR
AU - Toffalori, Carlo
TI - An elementary class extending abelian-by-\( G \) groups, for \( G \) infinite
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/12//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 4
SP - 213
EP - 217
AB - We show that for no infinite group \( G \) the class of abelian-by-\( G \) groups is elementary, but, at least when \( G \) is an infinite elementary abelian \( p \)-group (with \( p \) prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to \( G \) is elementary.
LA - eng
KW - Elementary class of structures; Abelian-by-G group; Commutator; abelian-by- group; elementary class; infinite group; elementarily equivalent; abelian group of prime exponent
UR - http://eudml.org/doc/244259
ER -