Structure of the Macdonald groups in one parameter

Alexander Montoya Ocampo; Fernando Szechtman

Structure of the Macdonald groups in one parameter

Group Theory 2024-01-11 v4

Authors: Alexander Montoya Ocampo , Fernando Szechtman

Abstract

Consider the Macdonald groups $G(\alpha)=\langle A,B\,|\, A^{[A,B]}=A^\alpha,\, B^{[B,A]}=B^\alpha\rangle$ , $\alpha\in{\mathbf Z}$ . We fill a gap in Macdonald's proof that $G(\alpha)$ is always nilpotent, and proceed to determine the order, upper and lower central series, nilpotency class, and exponent of $G(\alpha)$ .

Keywords

nilpotent groups finite group theory group theory

Cite

@article{arxiv.2302.07079,
  title  = {Structure of the Macdonald groups in one parameter},
  author = {Alexander Montoya Ocampo and Fernando Szechtman},
  journal= {arXiv preprint arXiv:2302.07079},
  year   = {2024}
}

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