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arXiv · 2609.23871

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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Primoz Moravec. 2026-09-20. Computing Bogomolov multipliers and finitary Bogomolov multipliers of infinite groups. https://arxiv.org/abs/2609.23871

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