Sylow subgroups of the Macdonald group on 2 parameters

Fernando Szechtman

Sylow subgroups of the Macdonald group on 2 parameters

Group Theory 2025-02-11 v4

Authors: Fernando Szechtman

Abstract

Consider the Macdonald group $G(\alpha,\beta)=\langle A,B\,|\, A^{[A,B]}=A^\alpha,\, B^{[B,A]}=B^\beta\rangle$ , where $\alpha$ and $\beta$ are integers different from one. We fill a gap in Macdonald's original proof that $G(\alpha,\beta)$ is nilpotent, and find the order and nilpotency class of each Sylow subgroup of $G(\alpha,\beta)$ .

Keywords

Macdonald group Sylow subgroups nilpotency group presentation torsion

Cite

@article{arxiv.2405.10356,
  title  = {Sylow subgroups of the Macdonald group on 2 parameters},
  author = {Fernando Szechtman},
  journal= {arXiv preprint arXiv:2405.10356},
  year   = {2025}
}

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