derived series meaning in Hindi

Examples

1. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup.
2. If the derived series eventually arrives at the zero subalgebra, then the Lie algebra is solvable.
3. The derived series for Lie algebras is analogous to the derived series for commutator subgroups in group theory.
4. The derived series for Lie algebras is analogous to the derived series for commutator subgroups in group theory.
5. For a finite group, the derived series terminates in a perfect group, which may or may not be trivial.
6. For instance the derived series and lower central series are descending series, while the upper central series is an ascending series.
7. Within the magazine there was a comic strip, " The Adventures of Monitaur ", an anime-derived series.
8. For connected Lie groups, these definitions are the same, and the derived series of the Lie algebra is the Lie algebra of the derived series of ( closed ) subgroups.
9. For connected Lie groups, these definitions are the same, and the derived series of the Lie algebra is the Lie algebra of the derived series of ( closed ) subgroups.
10. For an infinite group, the derived series need not terminate at a finite stage, and one can continue it to infinite ordinal numbers via transfinite recursion, thereby obtaining the "'transfinite derived series "', which eventually terminates at the perfect core of the group.