Fitting’s theorem

Fitting’s Theorem states that if G is a group and M and N are normal nilpotent subgroupsMathworldPlanetmathPlanetmath ( of G, then MN is also a normal nilpotent subgroup (of nilpotency class less than or equal to the sum of the nilpotency classes of M and N).

Thus, any finite groupMathworldPlanetmath has a unique largest normal nilpotent subgroup, called its Fitting subgroupMathworldPlanetmath. More generally, the Fitting subgroup of a group G is defined to be the subgroup of G generated by the normal nilpotent subgroups of G; Fitting’s Theorem shows that the Fitting subgroup is always locally nilpotent. A group that is equal to its own Fitting subgroup is sometimes called a Fitting group.

Title Fitting’s theorem
Canonical name FittingsTheorem
Date of creation 2013-03-22 13:51:39
Last modified on 2013-03-22 13:51:39
Owner yark (2760)
Last modified by yark (2760)
Numerical id 12
Author yark (2760)
Entry type Theorem
Classification msc 20D25
Defines Fitting subgroup
Defines Fitting group