Some supercharacter theories of a certain group of order $6n$

Document Type : Research Paper

Author

Department of Mathematics and Computer Science, Kharazmi University, Tehran, Iran

Abstract

In this paper, we are going to obtain some normal supercharacter theories of a group of order $6n$ with the presentation  $ U_{6n} = <a, b: a^{2n} = b^{3 } = 1, a^{-1}ba = b^{-1}>$ in special cases.  We will  also prove  that the automorphic supercharacter theories of this group can be computed  with the other methods.

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References

[1] Aliniaeifard, F. (2017). Normal supercharacter theories and their supercharacters. Journal of Algebra, 469, 464-484. https://doi.org/10.1016/j.jalgebra.2016.09.005
[2] Andre, C. (1995). Basic characters of the unitriangular group. Journal of algebra, 175(1), 287-319. https://doi.org/10.1006/jabr.1995.1187
[3] Burkett, S. T., & Lewis, M. L. (2020). Vanishing-o  subgroups and supercharacter theory products. International Journal of Algebra and Computation, 30(5), 1057-1072. https://doi.org/10.1142/S0218196720500307
[4] Darafsheh, M. R., & Yaghoobian, M. (2017). Tetravalent normal edge-transitive cayley graphs on a certain group of order 6n. Turkish Journal of Mathematics, 41(5), 1354-1359. https://doi.org/10.3906/mat-1504-39
[5] Diaconis, P., & Isaacs, I. (2008). Supercharacters and superclasses for algebra groups. Transactions of the American Mathematical Society, 360(5), 2359-2392. https://doi.org/10.1090/S0002-9947-07-04365-6
[6] Dornho , L. (1971). Group representation theory, part A. Marcel Dekker.
[7] Hendrickson, A. O. (2008). Supercharacter theories of  nite cyclic groups [Unpublished PhD. thesis]. Wisconsin University.
[8] Hendrickson, A. O. (2012). Supercharacter theory constructions corresponding to schur ring products. Communications in Algebra, 40(12), 4420-4438. https://doi.org/10.1080/00927872.2011.602999
[9] James, G., & Liebeck, M. (2001). Representations and characters of groups (2nd ed.). Cambridge University Press.
[10] Shelash, H. B., & Ashra , A. R. (2021). The number of subgroups of a given type in certain  nite groups. Iranian Journal of Mathematical Sciences and Informatics, 16(2), 73-87. https://doi.org/10.52547/ijmsi.16.2.73
[11] Yan, N. (2001). Representation theory of the  nite unipotent linear [Unpublished PhD. thesis]. Pennsylvania University.

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History

  • Receive Date: 02 September 2023
  • Revise Date: 14 November 2023
  • Accept Date: 02 December 2023

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