Robinson, Derek J. S. On inert subgroups of a group. (English) Zbl 1167.20319 Rend. Semin. Mat. Univ. Padova 115, 137-159 (2006). Summary: A subgroup \(H\) of a group \(G\) is called inert if \(|H:H\cap H^g|\) is finite for all \(g\) in \(G\). If every subgroup of \(G\) is inert, then \(G\) is said to be inertial. After giving an account of the basic properties of inert subgroups, we study the structure of inertial soluble groups. A classification is obtained for the groups which are finitely generated or have finite Abelian total rank. Cited in 1 ReviewCited in 10 Documents MSC: 20E07 Subgroup theorems; subgroup growth 20F16 Solvable groups, supersolvable groups 20F05 Generators, relations, and presentations of groups Keywords:subgroups of finite index; inert subgroups; soluble groups; finitely-generated groups; groups with finite Abelian total rank PDFBibTeX XMLCite \textit{D. J. S. Robinson}, Rend. Semin. Mat. Univ. Padova 115, 137--159 (2006; Zbl 1167.20319) Full Text: EuDML Link References: [1] V. V. BELYAEV, Locally finite simple groups represented as the product of two inert subgroups, Algebra and Logic, 31 (1993), pp. 216-221. Zbl0811.20041 MR1286336 · Zbl 0811.20041 · doi:10.1007/BF02259853 [2] V. V. BELYAEV, Inert subgroups in infinite simple groups, Siberian Math. J., 34 (1993), pp. 218-232. Zbl0836.20051 MR1248784 · Zbl 0836.20051 · doi:10.1007/BF00975160 [3] V. V. BELYAEV - M. KUZUCUOĞLU - E. SEÇKIN, Totally inert groups, Rend. Sem. Mat. Univ. Padova, 102 (1999), pp. 151-156. Zbl0945.20022 MR1739538 · Zbl 0945.20022 [4] J. C. LENNOX - D. J. S. ROBINSON, Soluble products of nilpotent groups, Rend. Sem. Mat. Univ. Padova, 62 (1980), pp. 261-280. Zbl0441.20026 MR582956 · Zbl 0441.20026 [5] J. C. LENNOX - D. J. S. ROBINSON, The Theory of Infinite Soluble Groups, Oxford 2004. Zbl1059.20001 MR2093872 · Zbl 1059.20001 [6] B. MAJCHER-IWANOW, Inert subgroups of uncountable locally finite groups, Comment. Math. Univ. Carolin., 44 (2003), pp. 615-622. Zbl1101.20023 MR2062877 · Zbl 1101.20023 [7] S. E. STONEHEWER, Permutable subgroups of infinite groups, Math. Z., 125 (1972), pp. 1-16. Zbl0219.20021 MR294510 · Zbl 0219.20021 · doi:10.1007/BF01111111 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.