Central series

From Groupprops

Jump to: navigation, search
This article defines a property that can be evaluated for a subgroup series
View a complete list of properties of subgroup series

Contents

Definition

A subgroup series:

G = K_1 \ge K_2 \ge \dots K_c \ge K_{c+1} = 1

is termed a central series if it satisfies the following conditions:

  1. It is a normal series: every Ki is normal in G
  2. For every i, Ki / Ki + 1 is contained in the center of G / Ki + 1.

Equivalently, it should satisfy the condition that for every i:

[G,K_i] \subset K_{i+1}

Equivalence of definitions

Further information: Equivalence of definitions of central series

Relation with other properties

Stronger properties

Weaker properties

Facts about Central seriesRDF feed
Stronger thanNormal series  +, and Subnormal series  +
Weaker thanStrongly central series  +
Retrieved from "http://groupprops.subwiki.org/wiki/Central_series"
Personal tools