Geodesic
Metabelian Products of Groups
Algebra i logika, Tome 43 (2004) no. 3, pp. 341-352.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove a number of facts on metabelian products of metabelian groups, useful in algebraic geometry over groups. Namely, for a metabelian product of arbitrary metabelian groups, we look at the structure of a derived subgroup, and the Fitting radical; find criteria determining when a metabelian product of $u$-groups is again a $u$-group; and specify conditions under which a metabelian product of metabelian groups is a strong semidomain.
Keywords: metabelian group, metabelian product, derived subgroup, Fitting radical, strong semidomain.
Mots-clés : $u$-group 
@article{AL_2004_43_3_a3,
     author = {V. N. Remeslennikov and N. S. Romanovskii},
     title = {Metabelian {Products} of {Groups}},
     journal = {Algebra i logika},
     pages = {341--352},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2004_43_3_a3/}
}
TY  - JOUR
AU  - V. N. Remeslennikov
AU  - N. S. Romanovskii
TI  - Metabelian Products of Groups
JO  - Algebra i logika
PY  - 2004
SP  - 341
EP  - 352
VL  - 43
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2004_43_3_a3/
LA  - ru
ID  - AL_2004_43_3_a3
ER  - 
%0 Journal Article
%A V. N. Remeslennikov
%A N. S. Romanovskii
%T Metabelian Products of Groups
%J Algebra i logika
%D 2004
%P 341-352
%V 43
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2004_43_3_a3/
%G ru
%F AL_2004_43_3_a3
V. N. Remeslennikov; N. S. Romanovskii. Metabelian Products of Groups. Algebra i logika, Tome 43 (2004) no. 3, pp. 341-352. http://geodesic.mathdoc.fr/item/AL_2004_43_3_a3/

[1] G. Baumslag, A. Myasnikov, V. Remeslennikov, “Algebraic geometry over groups. I. Algebraic sets and ideal theory”, J. Algebra, 219:1 (1999), 16–79 | DOI | MR | Zbl

[2] A. Myasnikov, V. Remeslennikov, “Algebraic geometry over groups. II. Logical foundations”, J. Algebra, 234:1 (2000), 225–276 | DOI | MR | Zbl

[3] V. Remeslennikov, R. Stohr, On the quasivariety generated by a non-cyclic free metabelian group, preprint 2001/20, Manchester Centre Pure Math., Manchester, 2001 | MR

[4] V. N. Remeslennikov, V. G. Sokolov, “Nekotorye svoistva vlozheniya Magnusa”, Algebra i logika, 9:5 (1970), 566–578 | MR | Zbl

[5] N. S. Romanovskii, “O nekotorykh algoritmicheskikh problemakh dlya razreshimykh grupp”, Algebra i logika, 13:1 (1974), 26–34 | MR | Zbl

[6] A. L. Shmelkin, “O svobodnykh proizvedeniyakh grupp”, Matem. sb., 79(121):4(8) (1969), 616–620

[7] N. S. Romanovskii, “O vlozheniyakh Shmelkina dlya abstraktnykh i prokonechnykh grupp”, Algebra i logika, 38:5 (1999), 598–612 | MR | Zbl

[8] O. Chapuis, “$\forall$-free metabelian groups”, J. Symb. Log., 62:1 (1997), 159–174 | DOI | MR | Zbl

[9] E. I. Timoshenko, “Ob universalnykh teoriyakh metabelevykh grupp i vlozhenii Shmelkina”, Sib. matem. zh., 42:5 (2001), 1168–1175 | MR | Zbl