Geodesic
Everywhere Dense Subgroups of One Group of Tree Automorphisms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 356-367.

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The well-known question of the existence, in the Grigorchuk 2-groups, of subgroups that are everywhere dense in the profinite topology is answered negatively. This is shown to be equivalent to the fact that these groups do not contain maximal subgroups of infinite index. 
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E. L. Pervova. Everywhere Dense Subgroups of One Group of Tree Automorphisms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 356-367. http://geodesic.mathdoc.fr/item/TM_2000_231_a13/

[1] Grigorchuk R. I., “K probleme Bernsaida o periodicheskikh gruppakh”, Funkts. analiz i ego pril., 14:1 (1980), 53–54 | MR | Zbl

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

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

[4] Suschanskii V. I., “Periodicheskie $p$-gruppy podstanovok i neogranichennaya problema Bernsaida”, DAN SSSR, 247:3 (1979), 557–561 | MR

[5] Gupta N., Sidki S., “Some infinite $p$-groups”, Algebra i logika, 22:5 (1983), 584–589 | MR | Zbl

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

[7] Rozhkov A. V., “Tsentralizatory elementov v odnoi gruppe avtomorfizmov derevev”, Izv. RAN. Ser. mat., 57:6 (1993), 82–105 | MR | Zbl

[8] Grigorchuk R. I., “Stepeni rosta konechno porozhdennykh grupp i teoriya invariantnykh srednikh”, Izv. AN SSSR. Ser. mat., 48:5 (1984), 939–985 | MR

[9] Rozhkov A. V., “Maksimalnye lokalno konechnye podgruppy v gruppe Grigorchuka”, Mat. zametki, 63:4 (1998), 617–624 | MR | Zbl

[10] Rozhkov A. V., “Problema sopryazhennosti v odnoi gruppe avtomorfizmov beskonechnogo dereva”, Mat. zametki, 64:4 (1998), 592–597 | MR | Zbl

[11] Rozhkov A. V., AT-gruppy, Ucheb. posobie, Chelyabinsk, 1998

[12] Grigorchuk R. I., “On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata”, Groups St Andrews 1997 in Bath, I, LMS Lect. Note Ser., 260, eds. C. M. Campbell, E. F. Robertson, N. Ruskuc, G. C. Smith, Cambridge Univ. Press, Cambridge, 1999, 290–317 | MR | Zbl