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.

##### 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 |

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\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)

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##### 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 |

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