zbMATH — the first resource for mathematics

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).

06F15 Ordered groups
20F60 Ordered groups (group-theoretic aspects)
Full Text: DOI
[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
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.