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Lie nilpotency index of skew symmetric elements in group algebras

  • Zsolt Adam Balogh
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Abstract

Let FG be the group algebra of a finite p-group G over a finite field F of characteristic p, where p is an odd prime. Let * be the classical involution of FG and let FG- be the Lie subalgebra of the skew symmetric elements with respect to *. In this paper, we prove that the Lie nilpotency index of FG is determined by its Lie subalgebra FG-, in the case when G is a p-group with a commutator subgroup of order p. The structure of the terms of the lower Lie central series of FG- has also been described.

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Cite

BibTeXRIS
BibTeX
@misc{balogh2026nilpotency,
  title = {{Lie nilpotency index of skew symmetric elements in group algebras}},
  author = {Zsolt Adam Balogh},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30408},
  eprint = {2608.30408},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30408},
}
RIS
TY  - UNPB
TI  - Lie nilpotency index of skew symmetric elements in group algebras
AU  - Zsolt Adam Balogh
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30408
UR  - https://arxiv.org/abs/2608.30408
AB  - Let FG be the group algebra of a finite p-group G over a finite field F of characteristic p, where p is an odd prime. Let * be the classical involution of FG and let FG^- be the Lie subalgebra of the skew symmetric elements with respect to *. In this paper, we prove that the Lie nilpotency index of FG is determined by its Lie subalgebra FG^-, in the case when G is a p-group with a commutator subgroup of order p. The structure of the terms of the lower Lie central series of FG^- has also been described.
ER  -