# Difference between revisions of "Fitting series"

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The fastest possible descending Fitting series for a [[finite solvable group]] is the [[lower Fitting series]], defined by iterating the [[nilpotent residual]]. For infinite solvable groups, there may or may not be a fastest possible descending Fitting series. | The fastest possible descending Fitting series for a [[finite solvable group]] is the [[lower Fitting series]], defined by iterating the [[nilpotent residual]]. For infinite solvable groups, there may or may not be a fastest possible descending Fitting series. | ||

− | The fastest possible ascending Fitting series is the [[upper Fitting series]]. | + | The fastest possible ascending Fitting series for a [[finite solvable group]] is the [[upper Fitting series]]. |

## Latest revision as of 14:58, 11 September 2011

## Definition

A **Fitting series** or **nilpotent series** for a solvable group is a subnormal series (of finite length?) where each quotient between successive groups is a nilpotent group.

The fastest possible descending Fitting series for a finite solvable group is the lower Fitting series, defined by iterating the nilpotent residual. For infinite solvable groups, there may or may not be a fastest possible descending Fitting series.

The fastest possible ascending Fitting series for a finite solvable group is the upper Fitting series.