Hartung, René Coset enumeration for certain infinitely presented groups. (English) Zbl 1235.20031 Int. J. Algebra Comput. 21, No. 8, 1369-1380 (2011). Summary: We describe an algorithm that computes the index of a finitely generated subgroup in a finitely \(L\)-presented group provided that this index is finite. This algorithm shows that the subgroup membership problem for finite index subgroups in a finitely \(L\)-presented group is decidable. As an application, we consider the low-index subgroups of some self-similar groups including the Grigorchuk group, the twisted twin of the Grigorchuk group, the Grigorchuk super-group, and the Hanoi 3-group. Cited in 4 Documents MSC: 20F05 Generators, relations, and presentations of groups 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 68W30 Symbolic computation and algebraic computation 20E07 Subgroup theorems; subgroup growth 20E28 Maximal subgroups 20-04 Software, source code, etc. for problems pertaining to group theory Keywords:coset enumeration; recursive presentations; self-similar groups; Grigorchuk groups; low-index subgroups; infinite presentations; finite \(L\)-presentations; algorithms; finitely generated subgroups; subgroup membership problem; subgroups of finite index Software:NQL PDFBibTeX XMLCite \textit{R. Hartung}, Int. J. Algebra Comput. 21, No. 8, 1369--1380 (2011; Zbl 1235.20031) Full Text: DOI arXiv References: [1] DOI: 10.1016/S0021-8693(03)00268-0 · Zbl 1044.20015 · doi:10.1016/S0021-8693(03)00268-0 [2] DOI: 10.2140/pjm.2005.218.241 · Zbl 1120.20037 · doi:10.2140/pjm.2005.218.241 [3] DOI: 10.1142/S0218196708004871 · Zbl 1173.20023 · doi:10.1142/S0218196708004871 [4] Bartholdi L., Serdica Math. J. 28 pp 47– [5] DOI: 10.1016/S1570-7954(03)80078-5 · doi:10.1016/S1570-7954(03)80078-5 [6] Bartholdi L., Internat. J. Algebra Comput. 24 pp 465– [7] DOI: 10.1215/S0012-7094-05-13012-5 · Zbl 1104.43002 · doi:10.1215/S0012-7094-05-13012-5 [8] DOI: 10.1017/S0004972700046955 · Zbl 0216.08603 · doi:10.1017/S0004972700046955 [9] de la Harpe P., Chicago Lectures in Mathematics, in: Topics in Geometric Group Theory (2000) · Zbl 0965.20025 [10] DOI: 10.4153/CJM-1974-072-0 · Zbl 0271.20018 · doi:10.4153/CJM-1974-072-0 [11] DOI: 10.2140/pjm.1963.13.775 · Zbl 0124.26402 · doi:10.2140/pjm.1963.13.775 [12] DOI: 10.1007/3-7643-7447-0_5 · doi:10.1007/3-7643-7447-0_5 [13] DOI: 10.1016/j.crma.2006.02.001 · Zbl 1135.20016 · doi:10.1016/j.crma.2006.02.001 [14] Grigorchuk R. I., Funktsional. Anal. i Prilozhen. 14 pp 53– [15] DOI: 10.1112/S1461157009000229 · Zbl 1243.20043 · doi:10.1112/S1461157009000229 [16] DOI: 10.1017/S0004972700018529 · Zbl 0985.20019 · doi:10.1017/S0004972700018529 [17] DOI: 10.1007/BF02809895 · Zbl 0991.20031 · doi:10.1007/BF02809895 [18] DOI: 10.1007/978-3-642-61896-3 · doi:10.1007/978-3-642-61896-3 [19] Lysënok I. G., Mat. Zametki 38 pp 634– [20] Neumann B. H., Math. Intell. 2 pp 17– [21] DOI: 10.1007/s10240-002-0006-7 · Zbl 1050.20019 · doi:10.1007/s10240-002-0006-7 [22] Pervova E. L., Tr. Mat. Inst. Steklova (Din. Sist., Avtom. i Beskon. Gruppy) 231 pp 356– [23] DOI: 10.1017/CBO9780511574702 · doi:10.1017/CBO9780511574702 [24] DOI: 10.1017/S0013091500008221 · Zbl 0015.10103 · doi:10.1017/S0013091500008221 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.