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单词 FittingsTheorem
释义

Fitting’s theorem


Fitting’s Theorem states that if G is a groupand M and N are normal nilpotent subgroupsMathworldPlanetmathPlanetmath (http://planetmath.org/Subgroup) of G,then MN is also a normal nilpotent subgroup(of nilpotency class less than or equal tothe 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.

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更新时间:2025/5/4 9:48:53