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Sylow subgroups exist
Difficulty level 3  +
Fact about Finite group (?)  + , Sylow subgroup (?)  +
Page class Fact  +
Proof style tabular  +
Uses Lucas' theorem + , Lucas' theorem prime power case + , Fundamental theorem of group actions + , Lagrange's theorem + , Class equation of a group + , Cauchy's theorem for abelian groups + , Central implies normal +
Modification dateThis property is a special property in this wiki. 20 August 2011 07:43:04  +
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Deducing basic facts about Sylow subgroups and Hall subgroups + Survey article about
Cauchy's theorem + , Congruence condition on Sylow numbers in terms of maximal Sylow intersection + , Equivalence of definitions of Sylow subgroup of normal subgroup + , Equivalence of definitions of universal congruence condition + , Every Sylow subgroup intersects the center nontrivially or is contained in a centralizer + , Every p-subgroup is conjugate to a p-subgroup whose normalizer in the Sylow is Sylow in its normalizer + , Every p-subgroup is well-placed in some Sylow subgroup + , Hall implies join of Sylow subgroups + , Hall subgroups exist in finite solvable + , Maximal Sylow intersection is tame + , Normal Hall implies permutably complemented + , Order has only two prime factors implies solvable + , Order of simple non-abelian group divides factorial of every Sylow number + , Order of simple non-abelian group divides half the factorial of every Sylow number + , Pi-dominating pi-subgroup implies pi-Hall + , Sylow implies order-dominated + , Sylow's theorem with operators + , Symmetric group on finite set has Sylow subgroup of prime order + , Three solvable subgroups of pairwise coprime indexes implies solvable + Uses
 

 

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