an:00652167
Zbl 0831.20033
Belyaev, V. V.
Inert subgroups in infinite simple groups
EN
Sib. Math. J. 34, No. 4, 606-611 (1993); translation from Sib. Mat. Zh. 34, No. 4, 17-23 (1993).
00016796
1993
j
20E07 20E32 20F50 20F24 20E15
subgroups of finite index; normal subgroups; inert subgroups; simple groups
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.