an:06189473
Zbl 1288.06023
Kopytov, V. M.
Arrangement of normal subgroups in ordered groups
EN
Algebra Logic 51, No. 6, 487-495 (2013); translation from Algebra Logika 51, No. 6, 734-747 (2012).
00316647
2013
j
06F15
linearly ordered group; normal subgroup; quotient group; infrainvariant system of subgroups
Summary: We look into the problem of determining the arrangement of normal (not necessarily relatively complex) subgroups \(A\) of a linearly ordered group \(G\) with respect to a system \(\mathcal L(G)\) of convex subgroups and describing the structure of quotient groups \(G/A\) with the aid of notions of the theory of linearly ordered groups. A characterization of quotient groups is obtained for groups possessing an infrainvariant system of subgroups. For the class of linearly ordered groups, as well as for certain of the classes close to it, answers to some known particular questions have been found.