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On some questions of the theory of partially ordered groups. (English. Russian original) Zbl 0536.06016
Algebra Logic 22, 316-321 (1983); translation from Algebra Logika 22, No. 4, 435-442 (1983).
The main results of this paper are as follows. It is proved that in each \(\ell\)-group there exists a largest convex locally nilpotent \(\ell\)- subgroup. There is constructed a linearly orderable group G having a subgroup H of finite index with a nilpotent commutant such that the commutant of G fails to be nilpotent. A partial solution of question 12 in the problem list [Notices Am. Math. Soc. 29, 327 (1982)] is given.
Reviewer: J.JakubĂ­k
06F15 Ordered groups
20F60 Ordered groups (group-theoretic aspects)
20E07 Subgroup theorems; subgroup growth
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