Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups

Oger, Francis

Oger, Francis

J. Symbolic Logic, Tome 66 (2001) no. 1, p. 1471-1480 / Harvested from Project Euclid

Résumé

We show that two abelian-by-finite groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. We also prove that abelian-by-finite groups satisfy a quantifier elimination property. On the other hand, for each integer n, we give some examples of nilpotent groups which satisfy the same sentences with n alternations of quantifiers and do not satisfy the same sentences with n + 1 alternations of quantifiers.

Publié le : 2001-09-14
Classification:

@article{1183746572,
     author = {Oger, Francis},
     title = {Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups},
     journal = {J. Symbolic Logic},
     volume = {66},
     number = {1},
     year = {2001},
     pages = { 1471-1480},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746572}
}

Oger, Francis. Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups. J. Symbolic Logic, Tome 66 (2001) no. 1, pp.  1471-1480. http://gdmltest.u-ga.fr/item/1183746572/