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  "body": "\n## Statement\n\nAny finite group that has a Hall *π*-subgroup for every set of primes *π* is solvable. This is a generalization of [[Burnside's theorem|0FMAQSB1SC]] that any group whose order is of the form *p\u003csup\u003ea\u003c/sup\u003eq\u003csup\u003eb\u003c/sup\u003e* for primes *p* and *q* is solvable, because Sylow's theorem implies that all Hall subgroups exist. This does not (at present) give another proof of Burnside's theorem, because Burnside's theorem is used to prove this [[converse|09A3N7ZN5G]].\n",
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