composition series


For groups

A composition series for a group, GG, is a subnormal series, (that is, a sequence of subgroups, each a normal subgroup of the next one) such that each factor group H i+1/H iH_{i+1} / H_i is a simple group.

In an abelian category

An object XX of an abelian category has a composition series if there is a chain of subobjects

0=X 0<X 1<<X n1<X n=X0= X_0 \lt X_1 \lt\ldots \lt X_{n-1} \lt X_n = X

such that X i/X i1X_i / X_{i-1} is simple for 1in1\leq i\leq n.

See at length of an object for more

Last revised on November 3, 2016 at 05:03:30. See the history of this page for a list of all contributions to it.