Generalized solvable group
From Encyclopedia of Mathematics - Reading time: 1 min
A group from one of the generalized solvable classes of groups. A class of groups is called generalized solvable if it contains all solvable groups (cf. Solvable group) and if its intersection with the class of finite groups is the class of all finite solvable groups. Quite a number of classes of generalized solvable groups have been considered; principally, the connections between them have been studied. The most important class of generalized solvable groups is the class of locally solvable groups (cf. Locally solvable group). Other classes have been introduced in the study of various properties of normal and subnormal series (see [1], [2]).
References[edit]
| [1] | A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian) |
| [2] | A.G. Kurosh, S.N. Chernikov, "Solvable and nilpotent groups" Uspekhi Mat. Nauk , 2 : 3 (1947) pp. 18–59 (In Russian) |
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