# Jordan-Hölder decomposition

A Jordan–Hölder decomposition of a group $G$ is a filtration

 $G=G_{1}\supset G_{2}\supset\cdots\supset G_{n}=\{1\}$

such that $G_{i+1}$ is a normal subgroup of $G_{i}$ and the quotient $G_{i}/G_{i+1}$ is a simple group for each $i$.

Title Jordan-Hölder decomposition JordanHolderDecomposition 2013-03-22 12:08:41 2013-03-22 12:08:41 djao (24) djao (24) 9 djao (24) Definition msc 20E15 composition series DerivedSubgroup JordanHolderDecompositionTheorem