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Centroids Of Partially Commutative Two-step Nilpotent Groups

  • Ivan M. Buchinskiy
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Abstract

In this paper, we describe the centroid (according to S. Lioutikov and A. Myasnikov) of an arbitrary finitely generated graph two-step nilpotent Hall exponential group over a binomial domain whose commutativity graph has no central vertices. Based on this description, we prove that if the non-commutativity graph of such a group has exactly one connected component and the group is non-Abelian, then the group is rigid.

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Cite

BibTeXRIS
BibTeX
@misc{buchinskiy2026centroids,
  title = {{Centroids Of Partially Commutative Two-step Nilpotent Groups}},
  author = {Ivan M. Buchinskiy},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40680},
  eprint = {2610.40680},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40680},
}
RIS
TY  - UNPB
TI  - Centroids Of Partially Commutative Two-step Nilpotent Groups
AU  - Ivan M. Buchinskiy
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.40680
UR  - https://arxiv.org/abs/2610.40680
AB  - In this paper, we describe the centroid (according to S. Lioutikov and A. Myasnikov) of an arbitrary finitely generated graph two-step nilpotent Hall exponential group over a binomial domain whose commutativity graph has no central vertices. Based on this description, we prove that if the non-commutativity graph of such a group has exactly one connected component and the group is non-Abelian, then the group is rigid.
ER  -