Belyaev, V. V. Inert subgroups in infinite simple groups. (English. Russian original) Zbl 0831.20033 Sib. Math. J. 34, No. 4, 606-611 (1993); translation from Sib. Mat. Zh. 34, No. 4, 17-23 (1993). Subgroups \(A\) and \(B\) of a group \(G\) are called commensurable if \(A \cap B\) is a subgroup of finite index in \(A\) as well as in \(B\). If a subgroup is commensurable with each of its conjugate subgroups in \(G\) then we call \(A\) inert in \(G\) (the term “inert subgroup” was proposed by O. H. Kegel). The present paper is devoted to the study of the relation between the structure of normal subgroups in an inert subgroup and the normal structure of the entire group. We apply the results obtained in this direction to examine the structure of inert subgroups in simple groups. Cited in 13 Documents MSC: 20E07 Subgroup theorems; subgroup growth 20E32 Simple groups 20F50 Periodic groups; locally finite groups 20F24 FC-groups and their generalizations 20E15 Chains and lattices of subgroups, subnormal subgroups Keywords:subgroups of finite index; normal subgroups; inert subgroups; simple groups PDFBibTeX XMLCite \textit{V. V. Belyaev}, Sib. Math. J. 34, No. 4, 606--611 (1993; Zbl 0831.20033); translation from Sib. Mat. Zh. 34, No. 4, 17--23 (1993) Full Text: DOI References: [1] V. V. Belyaev, ?Locally finite groups containing a finite inseparable subgroup,? Sibirsk. Mat. Zh.,34, No. 2, 23-41 (1993). · Zbl 0836.20051 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.