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Completion of invariant locally nilpotent subgroups of fully ordered groups. (English. Russian original) Zbl 0794.06013
Math. Notes 51, No. 2, 129-132 (1992); translation from Mat. Zametki 51, No. 2, 35-39 (1992).
It is proved that any fully ordered (FO) group \(G\) with an invariant locally nilpotent subgroup \(H\) admits an order-preserving embedding into a fully ordered group \(G^*\) with an invariant locally nilpotent complete subgroup \(H^*\) such that \(H\leq H^*\). In particular, this solves Problem 1.61 in the Kourovka notebook, 9th ed. (1984; Zbl 0552.20001).

MSC:
06F15 Ordered groups
20F60 Ordered groups (group-theoretic aspects)
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[1] Kovrova Notebook. Unsolved Problems of Group Theory [in Russian], Novosibirsk (1984).
[2] A. I. Kokorin and V. M. Kopytov, Fully Ordered Groups [in Russian], Nauka, Moscow (1972). · Zbl 0192.36401
[3] A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).
[4] C. D. Fox, ”The problem of adjoining roots of ordered groups,” Bull. Austral. Math. Soc.,11, No. 1, 157–158 (1974). · Zbl 0278.06014 · doi:10.1017/S0004972700043720
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