November 8, 2025Open Access

Algorithms for twisted conjugacy classes of polycyclic-by-finite groups II

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The algorithm determines whether the Reidemeister number is finite for homomorphisms, and returns twisted conjugacy representatives.
Primary findings show that applying the algorithm can compute double cosets and orbits effectively.
Observational analysis provides a method to evaluate twisted conjugacy classes of polycyclic-by-finite groups.
This approach may highlight new computational advances in group theory applications, expanding existing algorithms.

Implication

Analysis reveals that homomorphisms impact the Reidemeister number for twisted conjugacy classes, suggesting a new computational method.

Abstract

We construct an algorithm that, given a pair of homomorphisms between polycyclic-by-finite groups, determines whether their Reidemeister number is finite, and additionally returns a set of representatives of the twisted conjugacy classes if it is. Moreover, we show how this algorithm can be applied to compute double cosets and orbits of affine actions.

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Cite This Study

Sam Tertooy (2025) studied this question.

synapsesocial.com/papers/690e8b75a5b062d7a4e737d8 https://doi.org/10.48550/arxiv.2504.03596

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Implication

Analysis reveals that homomorphisms impact the Reidemeister number for twisted conjugacy classes, suggesting a new computational method.

Algorithms for twisted conjugacy classes of polycyclic-by-finite groups II

Key Points

Implication

Abstract

Discussion

Cite This Study

Algorithms for twisted conjugacy classes of polycyclic-by-finite groups II

Key Points

Implication

Abstract

Discussion

Cite This Study

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