Lower and Upper Lie Nilpotency Indices of Modular Group Algebras

@misc{gildea2026lower,
  title = {{Lower and Upper Lie Nilpotency Indices of Modular Group Algebras}},
  author = {Joe Gildea},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10915},
  eprint = {2610.10915},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10915},
}

TY  - UNPB
TI  - Lower and Upper Lie Nilpotency Indices of Modular Group Algebras
AU  - Joe Gildea
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10915
UR  - https://arxiv.org/abs/2610.10915
AB  - We resolve the remaining cases of a longstanding problem on the lower and upper Lie nilpotency indices of modular group algebras. Equality of the two indices has been known in characteristics greater than three since 1992; we establish it in the remaining characteristics two and three, thereby completing the problem for finite groups of prime-power order over finite fields. The proof gives a uniform argument for every prime and introduces a terminal restricted Poincare-Birkhoff-Witt construction that converts the lower-Lie problem into a chronological reachability argument, with no structural hypothesis on the derived subgroup.
ER  -