let math g math group math xy x xy math commutator operation let math g g supseteq g supseteq g supseteq cdots supseteq g n supseteq cdots math central series math g math mdash commutator subgroup math g ig j math contained math g j math math ij math math l bigoplus g g math lie ring addition supplied group operation abelian homogeneous part bracket operation given math xg yg j xy g j math extended linearly centrality series ensures commutator math xy math gives bracket operation
Formal science Mathematics Pure mathematics Algebra Lie algebra