On stabilization of \(E_k\) chains. (English) Zbl 1473.20041
Summary: We study special subgroups of infinite groups that generalize double centralizers. We analyze sufficient conditions for descending chains of such subgroups to stop after finitely many steps. We discuss whether this phenomenon can happen in the class of groups satisfying chain condition on centralizers.
MSC:
| 20F22 | Other classes of groups defined by subgroup chains |
| 20B35 | Subgroups of symmetric groups |
| 20A15 | Applications of logic to group theory |
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
References:
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| [5] | Cakmak, T. |
| [6] | Wehrfritz, B. A. F., Infinite linear groups (1973) · Zbl 0261.20038 |
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