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Skew braces of size p2q2. The cyclic Sylow q-subgroup case

  • Teresa Crespo
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Abstract

We consider relatively prime integer numbers m and n such that each group of order mn has a normal subgroup of order m. We prove that any skew brace of size mn has an ideal of size m and, if the subgroup of order m of its additive group is abelian, a subbrace of size n. We give a method to classify skew braces of size mn, such that the subgroup of order m of their additive group is abelian, from the classification of braces of size m and the classification of skew braces of size n. We apply this result to determine all skew braces of size p2q2 of non-abelian type, for p and q odd primes, p<q, such that their ideal of order q2 is cyclic.

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Cite

BibTeXRIS
BibTeX
@misc{crespo2026skew,
  title = {{Skew braces of size $p^2q^2$. The cyclic Sylow $q$-subgroup case}},
  author = {Teresa Crespo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.24655},
  eprint = {2609.24655},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24655},
}
RIS
TY  - UNPB
TI  - Skew braces of size p^2q^2. The cyclic Sylow q-subgroup case
AU  - Teresa Crespo
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.24655
UR  - https://arxiv.org/abs/2609.24655
AB  - We consider relatively prime integer numbers m and n such that each group of order mn has a normal subgroup of order m. We prove that any skew brace of size mn has an ideal of size m and, if the subgroup of order m of its additive group is abelian, a subbrace of size n. We give a method to classify skew braces of size mn, such that the subgroup of order m of their additive group is abelian, from the classification of braces of size m and the classification of skew braces of size n. We apply this result to determine all skew braces of size p^2q^2 of non-abelian type, for p and q odd primes, p<q, such that their ideal of order q^2 is cyclic.
ER  -