Skip to content

feat: add Burnside normal p-complement theorem eval problem#312

Closed
kim-em wants to merge 1 commit into
mainfrom
eval/burnside-normal-p-complement
Closed

feat: add Burnside normal p-complement theorem eval problem#312
kim-em wants to merge 1 commit into
mainfrom
eval/burnside-normal-p-complement

Conversation

@kim-em
Copy link
Copy Markdown
Collaborator

@kim-em kim-em commented May 24, 2026

This PR adds Burnside's normal p-complement theorem (1911): if a Sylow p-subgroup P of a finite group G is central in its normalizer, then G has a normal p-complement. The prototype transfer-based local-to-global argument and the seed of fusion theory.

Mathlib already contains the underlying construction MonoidHom.ker_transferSylow_isComplement'; the eval problem is to assemble the named theorem statement from that machinery.

🤖 Prepared with Claude Code

This PR adds Burnside's normal p-complement theorem (1911): if a Sylow
p-subgroup P of a finite group G is central in its normalizer, then G
has a normal p-complement. The prototype transfer-based local-to-global
argument and the seed of fusion theory.

Mathlib already contains the underlying construction
`MonoidHom.ker_transferSylow_isComplement'`; the eval problem is to
assemble the named theorem statement from that machinery.

🤖 Prepared with Claude Code
@kim-em kim-em marked this pull request as ready for review May 24, 2026 08:15
@kim-em
Copy link
Copy Markdown
Collaborator Author

kim-em commented May 24, 2026

Closing: this statement is essentially already in Mathlib via MonoidHom.ker_transferSylow_isComplement' and MonoidHom.not_dvd_card_ker_transferSylow in Transfer.lean. The full proof is just 5 lines assembling those existing lemmas — see the spelled-out proof for the witness. As a benchmark this is an "API discovery" exercise rather than a theorem-proving challenge. Closing in favour of stronger results not in Mathlib (Hall's theorem for solvable groups, Frobenius's p-nilpotence, etc.) in a future PR.

@kim-em kim-em closed this May 24, 2026
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

1 participant