Geodesic
The Congruence Property of AT-Groups
Algebra i logika, Tome 41 (2002) no. 5, pp. 553-567.

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

An AT-group is said to possess the congruence property if every normal subgroup of that group contains a congruence subgroup. We construct a series of examples of periodic AT-groups without this property. Moreover, we give an example of a periodic group which has a decidable conjugacy problem but lacks conjugacy separability.
Mots-clés : AT-group
Keywords: periodic group, congruence property, conjugacy problem, conjugacy separability. 
@article{AL_2002_41_5_a2,
     author = {E. L. Pervova},
     title = {The {Congruence} {Property} of {AT-Groups}},
     journal = {Algebra i logika},
     pages = {553--567},
     publisher = {mathdoc},
     volume = {41},
     number = {5},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_5_a2/}
}
TY  - JOUR
AU  - E. L. Pervova
TI  - The Congruence Property of AT-Groups
JO  - Algebra i logika
PY  - 2002
SP  - 553
EP  - 567
VL  - 41
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2002_41_5_a2/
LA  - ru
ID  - AL_2002_41_5_a2
ER  - 
%0 Journal Article
%A E. L. Pervova
%T The Congruence Property of AT-Groups
%J Algebra i logika
%D 2002
%P 553-567
%V 41
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2002_41_5_a2/
%G ru
%F AL_2002_41_5_a2
E. L. Pervova. The Congruence Property of AT-Groups. Algebra i logika, Tome 41 (2002) no. 5, pp. 553-567. http://geodesic.mathdoc.fr/item/AL_2002_41_5_a2/

[1] S. V. Aleshin, “Konechnye avtomaty i problema Bernsaida o periodicheskikh gruppakh”, Matem. zametki, 11:3 (1972), 319–328 | MR | Zbl

[2] R. I. Grigorchuk, “Stepeni rosta konechno-porozhdennykh grupp i invariantnoe srednee”, Izv. AN SSSR. Ser. matem., 48:5 (1984), 939–985 | MR

[3] A. V. Rozhkov, “K teorii grupp aleshinskogo tipa”, Matem. zametki, 40:5 (1986), 572–589 | MR | Zbl

[4] R. I. Grigorchuk, “Just infinite branch groups”, New horizons in pro-$p$-groups, Progr. Math., 184, Birkhäuser Boston, Boston, MA, 2000, 121–179 | MR | Zbl

[5] A. V. Rozhkov, K teorii grupp aleshinskogo tipa, Dis. kand. fiz.-mat. nauk, 1986

[6] I. G. Lysenok, “Sistema opredelyayuschikh sootnoshenii dlya gruppy Grigorchuka”, Matem. zametki, 38:4 (1985), 503–516 | MR | Zbl

[7] R. I. Grigorchuk, “On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata”, Groups St. Andrews 1997 in Bath, v. I, London Math. Soc. Lecture Note Ser., 260, Cambridge Univ. Press, Cambridge, 1999, 290–317 | MR | Zbl

[8] R. Grigorchuk, J. Wilson, “The conjugacy problem for certain branch groups”, Trudy MIAN, 231, 2000, 215–230 | MR | Zbl