A computational technique for studying the Heisenberg group
*Saad O. BedaiwiCorresponding authorsaadowaidmath@uomustansiriyah.edu.iqDepartment of MathematicsCollege of ScienceMustansiriyah UniversityBaghdad, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 09 Aug 2022
- Published Online:
- 07 May 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1637
- Pages:
- 457–466
Abstract
Keywords
Subject Classifications
References
[1] J. Grassberger and G. Hörmann, “A note on representations of the finite Heisenberg group and sums of greatest common divisors”, Discrete Mathematics; Theoretical Computer Science, vol. 42 (2001). Available: https://doi.org/10.46298/dmtcs.284
[2] R. Howe, “On the role of the Heisenberg group in harmonic analysis”, Bulletin of the American Mathematical Society, vol. 3, no. 2, pp. 821-843 (1980). Available: https://doi.org/10.1090/s0273-0979-1980-14825-9
[3] V. Kisil, “The Heisenberg group in mathematics and physics [Slides]”. School of Mathematics University of Leeds (England) (2016). Available: http://www.maths.leeds.ac.uk/~kisilv.
[4] D. Rottensteiner, “Foundations of Harmonic Analysis on the Heisenberg Group (“Thesis”)”. University of Warwick (2010). Available: https://phaidra.univie.ac.at/open/o:1265111.
[5] S. Semmes, “An Introduction to Heisenberg Groups in Analysis and Geometry”, Notices of the AMS. Vol. 50(6), 640–646 (2003). Available: https://arxiv.org/pdf/1411.3861.pdf.
[6] D. J. S. Robinson, A Course in the theory of groups, 2nd ed. New Yourk, NY: Springer (2012).
[7] C. C. Sims, Computation with finitely Presented Groups (Encyclopedia of Mathematics and its Applications, Series Number 48). Cambridge University Press (1994).
[8] D. Segal, Polycyclic Groups (Cambridge Tracts in Mathematics, Series Number 82). Cambridge University Press (2005).
[9] S. K. Sinanan and D. F. Holt, “Algorithms for polycyclic-by-finite groups,” J. Symb. Comput., vol. 79, pp. 269–284 (2017). Available: https://doi.org/10.1016/j.jsc.2016.02.008
[10] B. Eick, “Computing the order and the index of a subgroup in a polycyclic group,” arXiv [math.GR] (2021). Available: https://arxiv.org/pdf/2102.04023.pdf.
[11] B. Höfling,”Efficient multiplication algorithms for finite polycyclic groups”. Conference Proceedings (2002). Available: http://www.icm.tu-bs.de/~bhoeflin/preprints/collect.pdf.
[12] Pankaj, Gunjan, and M. Pruthi, “Unit graphs and subgraphs of Symmetric, Quaternion and Heisenberg groups”, Journal of Information and Optimization Sciences, 38:1, pp. 207-218 (2017). Available: https://doi.org/10.1080/02522667.2016.1250455.
[13] B. Senoussi,”Helicoidal surfaces of finite type in the 3-dimensional” Heisenberg group, Journal of Interdisciplinary Mathematics, 25:4, PP. 1143-1152 (2022). Available: https://doi.org/10.1080/09720502.2021.1950287
[14] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.11.1 (2021). (https://www.gap-system.org).
[15] B.O. Eamonn, “Polycyclic groups” (2010). Available: https://www.icts.res.in/sites/default/files/1284624569notes.pdf
[16] G. Baumslag, F. B. Cannonito, D. J. S. Robinson, and D. Segal, “The algorithmic theory of polycyclic-by-finite groups,” J. Algebra, vol. 142, no. 1, pp. 118–149 (1991). Available: https://doi.org/10.1016/0021-8693(91)90221-s.
[17] E. Formanek, “Conjugate separability in polycyclic groups,” J. Algebra, vol. 42, no. 1, pp. 1–10 (1976). Available: https://doi.org/10.1016/0021-8693(76)90021-1.
[18] B. Eick, “Algorithms for Polycyclic Groups”, Habilitationsschrift, Universität Kassel (2001). Available: http://www.icm.tu-bs.de/~beick/publ/habil.pdf.
[19] J. Bray, M. Conder, C. Leedham-Green, and E. O’Brien, “Short presentations for alternating and symmetric groups,” Trans. Am. Math. Soc., vol. 363, no. 6, pp. 3277–3285 (2011). Available: https://doi.org/10.1090/s0002-9947-2011-05231-1.
[20] D. F. Holt, B. Eick, and E. A. Brien, Handbook of Computational Group Theory (Discrete Mathematics and Its Applications 24). Chapman and Hall/CRC (2005).
[21] C. R. Leedham-Green and L. H. Soicher, “Symbolic Collection using Deep Thought,” LMS J. Comput. Math., vol. 1, pp. 9–24 (1998). Available: https://doi.org/10.1112/s1461157000000127.
