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

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

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topToffalori, 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

top- HODGES, W., Model theory. Cambridge University Press, Cambridge1993. Zbl1139.03021MR1221741DOI10.1017/CBO9780511551574
- 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
- OGER, F., Axiomatization of the class of abelian-by-$G$ groups for a finite group $G$. Preprint, 1995.
- PREST, M., Model theory and modules. Cambridge University Press, Cambridge1988. Zbl0634.03025MR933092DOI10.1017/CBO9780511600562
- ROBINSON, D., A course in the theory of groups. Springer, New York1982. Zbl0836.20001MR648604

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