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单词 WielandtKegelTheorem
释义

Wielandt-Kegel theorem


Theorem.

If a finite groupMathworldPlanetmath is the productPlanetmathPlanetmath of two nilpotent subgroupsMathworldPlanetmathPlanetmath,then it is solvable.

That is, if H and K are nilpotent subgroups of a finite group G,and G=HK, then G is solvable.

This result can be considered asa generalizationPlanetmathPlanetmath of Burnside’s p-q Theorem (http://planetmath.org/BurnsidePQTheorem),because if a group G is of order pmqn, where p and q are distinct primes, then G is the product of a Sylow p-subgroup (http://planetmath.org/SylowPSubgroup) and Sylow q-subgroup, both of which are nilpotent.

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更新时间:2025/5/4 23:42:55