# composition series

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## composition series

[‚käm·pə′zish·ən ′sir‚ēz]
(mathematics)
A normal series G1, G2, …, of a group, where each Gi is a proper normal subgroup of Gi-1and no further normal subgroups both contain Gi and are contained in Gi-1.
References in periodicals archive ?
Among their topics are spherical varieties and perspectives in representation theory, on toric degenerations of flag varieties, derived categories of quasi-hereditary algebras and their derived composition series, bounded and semi-bounded representations of infinite dimensional Lie groups, and geometric invariant theory for principal three-dimensional subgroups acting on flag varieties.
My well-known paintings include The Blue Rider and the Composition series.
Multiliteracy Centers represents some of the finest work yet within the New Dimensions and Computers and Composition series on representing the complexity of multimodality in teaching and learning scenarios.
Given G = (X) [less than or equal to] GL(V), the goal is to compute quantitative and structural information about G such as the order, a composition series, and important characteristic subgroups like the largest solvable normal subgroup of G.
Babai and Beals define a series of characteristic subgroups, present in all finite groups, and initiate a program that tries to compute a composition series going through these characteristic subgroups.
In that paper, a Las Vegas algorithm is described that computes [absolute value of G] and a composition series, and sets up a data structure for membership testing in G.
Then a composition series for the C-module V is computed; if all composition factors are isomorphic then the tensor decomposition of V can be read from the embedding of composition factors in V and their identifications by the isomorphisms.
He introduces modules, then covers finely integrated modules and their application to Abelian groups, simple modules and composition series.
For n = 1, the maximal series of normal multi-group subspaces is just a composition series of a finite group.
By Jordan-Holder theorem, we know the length of this composition series is a constant, dependent only on ([G.
Jordan-Holder theorem) For a finite group G, the length of the composition series is a constant, only dependent on G.
His distinctive works consist mainly of horizontal and vertical lines forming various ninety - degree grids on a light background colored only with solid primary colors, as in his famous Composition series.

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