Conjugacy Classes of the Split Extension 28: U4(2)

References

[1] Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A. and Wilson, R.A. (1985). Atlas of Finite Groups. Oxford: Clarendon Press.

[2] Moori, J. and Basheer, A.B. (2015). A survey on Clifford-Fischer theory. London Mathematical Society Lecture Notes Series, 422, 160-172.

[3] Prins, A.L., Monaledi, R.L. and Fray, R.L. (2020). On a maximal subgroup (29: L3(4)): 3 of the automorphism group U6(2): 3 of U6(2). Afrika Matematika, 31, 1311-1336.

[4] Moori, J. and Zimba, K. (2017). Fischer-Clifford matrices of the generalized symmetric group-(a computational approach). Quaestiones Mathematicae, 40(1), 75-89.

[5] Musyoka, D.M., Njuguna, L.N., Prins, A.L. and Chikamai, L. (2022). On a maximal subgroup of the orthogonal group O+8(3). Proyecciones, 41(1), 137-161.

[6] Chileshe, C., Seretlo, T. and Moori, J. (2016). On a maximal parabolic subgroup of Sp8(2). Quaestiones Mathematicae, 39(1), 45-57.

[7] Fischer, B. (1991). Clifford matrices. In Representation theory of finite groups and finite-dimensional algebras (pp. 1-16). Birkhäuser, Basel.

[8] GAP – Groups, Algorithms, and Programming, Version 4.11.1. (2021). The GAP Group. (https://www.gap-system.org)

[9] Bosma, W., Cannon, J. and Playoust, C. (1997). The Magma algebra system I: The user language. Journal of Symbolic Computation, 24(3-4), 235-265.

[10] Holt, D.F., Eick, B. and O'Brien, E.A. (2005). Handbook of computational group theory. Chapman and Hall/CRC.

[11] James, G. and Liebeck, M. (2001). Representations and characters of groups. Cambridge University Press.

[12] Wilson, R.A. (2009). The finite simple groups. Graduate Texts in Mathematics, vol. 251. London: Springer.

[13] Lux, K. and Pahlings, H. (2010). Representations of groups: A computational approach. Cambridge University Press.

[14] Isaacs, I.M. (1976). Character theory of finite groups. Academic Press.

[15] Curtis, C.W. and Reiner, I. (1962). Representation theory of finite groups and associative algebras. New York: Interscience Publishers.

[16] Fulton, W. and Harris, J. (1991). Representation theory: a first course. Springer Science & Business Media.

[17] Gorenstein, D., Lyons, R. and Solomon, R. (1994). The classification of the finite simple groups. Mathematical Surveys and Monographs, vol. 40. American Mathematical Society.

[18] Aschbacher, M. (2000). Finite group theory. Cambridge University Press.

[19] Dixon, J.D. and Mortimer, B. (1996). Permutation groups. Springer Science & Business Media.

[20] Seress, Á. (2003). Permutation group algorithms. Cambridge University Press.

@article{1706209,
      author = {Wekesa Caroly Wafula, Lucy Walingo Chikamai, Vincent Nyongesa Marani},
      title = {Conjugacy Classes of the Split Extension 28: U4(2)},
      journal = {Iconic Research And Engineering Journals},
      year = {2024},
      volume = {8},
      number = {2},
      pages = {736-741},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1706209.pdf},
      abstract = {This study presents a comprehensive analysis of the conjugacy classes of the split extension 28: U4(2), where U4(2) is the unitary group of degree 4 over the field with 2 elements. Using a combination of theoretical techniques, including Fischer-Clifford matrices and character theory, along with computational tools such as GAP and MAGMA, we determined and classified all 49 conjugacy classes of this group. Our analysis revealed complex fusion patterns from U4(2) to 28: U4(2), including class splitting and the introduction of new element orders. We found that 28: U4(2) has more than double the number of conjugacy classes compared to U4(2) alone, with class sizes ranging from 5 to over 1.3 million elements. This work addresses significant gaps in the existing literature regarding this specific group extension and provides insights into its structure, representations, and automorphisms. The methodology and results presented here contribute to the broader understanding of group extensions and lay the groundwork for further investigations into the properties and applications of 28: U4(2) in areas such as coding theory and quantum mechanics.},
      keywords = {Conjugacy Classes, Split Extension},
      month = {August},
  }