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PreprintCC BY 4.0arXiv

Computing Bogomolov multipliers and finitary Bogomolov multipliers of infinite groups

  • Primoz Moravec
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Abstract

We study homological Bogomolov multipliers and finitary Bogomolov multipliers of infinite groups, with emphasis on polycyclic groups. We obtain structural descriptions for torsion-free nilpotent groups of class two, semidirect products, wreath products, and infinite simple groups. The class-two case reveals a connection with rational points on linear sections of Grassmannians, explaining an arithmetic obstruction to a general algorithm. On the positive side, we give a deterministic algorithm for virtually abelian polycyclic groups and an algorithm for finitary Bogomolov multipliers of arbitrary polycyclic groups, both implemented in GAP.

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Cite

BibTeXRIS
BibTeX
@misc{moravec2026computing,
  title = {{Computing Bogomolov multipliers and finitary Bogomolov multipliers of infinite groups}},
  author = {Primoz Moravec},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23871},
  eprint = {2609.23871},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23871},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Computing Bogomolov multipliers and finitary Bogomolov multipliers of infinite groups
AU  - Primoz Moravec
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23871
UR  - https://arxiv.org/abs/2609.23871
AB  - We study homological Bogomolov multipliers and finitary Bogomolov multipliers of infinite groups, with emphasis on polycyclic groups. We obtain structural descriptions for torsion-free nilpotent groups of class two, semidirect products, wreath products, and infinite simple groups. The class-two case reveals a connection with rational points on linear sections of Grassmannians, explaining an arithmetic obstruction to a general algorithm. On the positive side, we give a deterministic algorithm for virtually abelian polycyclic groups and an algorithm for finitary Bogomolov multipliers of arbitrary polycyclic groups, both implemented in GAP.
ER  -