An elementary class extending abelian-by- G groups, for G infinite

Carlo Toffalori

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 4, page 213-217
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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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 -

References

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  1. HODGES, W., Model theory. Cambridge University Press, Cambridge1993. Zbl1139.03021MR1221741DOI10.1017/CBO9780511551574
  2. MARCJA, A. - TOFFALORI, C., Abelian-by- G groups, for G finite, from the model theoretic point of view. Math. Log. Quart., 40, 1994, 125-131. Zbl0808.03020MR1284450DOI10.1002/malq.19940400117
  3. OGER, F., Axiomatization of the class of abelian-by- G groups for a finite group G . Preprint, 1995. 
  4. PREST, M., Model theory and modules. Cambridge University Press, Cambridge1988. Zbl0634.03025MR933092DOI10.1017/CBO9780511600562
  5. ROBINSON, D., A course in the theory of groups. Springer, New York1982. Zbl0836.20001MR648604

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