Normal supercharacter theory of the dihedral groups

Document Type : Original Article


Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran


Diaconis ‎and ‎Isaacs ‎defined ‎the ‎‎supercharacter ‎theory ‎for ‎finite ‎groups ‎as a‎ ‎natural ‎generalization ‎of ‎the ‎classical ‎ordinary ‎character ‎theory ‎of ‎finite ‎groups. ‎‎Supercharacter ‎theory ‎of ‎many ‎finite ‎groups ‎such ‎as ‎the ‎cyclic ‎groups, ‎the ‎Frobenius ‎groups, ‎etc. ‎were ‎well ‎studied ‎and ‎well-known. ‎In ‎this ‎paper ‎we ‎find ‎the ‎normal ‎and ‎automorphic ‎‎supercharacter ‎theories ‎of ‎the ‎dihedral ‎groups ‎in ‎special ‎cases.‎


Main Subjects

[1] F. Aliniaeifard, Normal supercharacter theories and their supercharacters, J. Algebra, 469 (2017), pp. 464– 484.
[2] C. A. M. Andre´, Basic characters of the unitriangular group, J. Algebra, 175 (1995), pp. 287–319.
[3] J. L. Brumbaugh, M. Bulkow, P. S. Fleming, L. A. Garcia German, S. R. Garcia, G. Karaali, M. Michal, A. P. Turner, and H. Suh, Supercharacters, exponential sums, and the uncertainty principle, J. Number Theory, 144 (2014), pp. 151–175.
[4] K. Conrad, Dihedral Groups II. Available online at: grouptheory/dihedral2.pdf, 2018.
[5] P. Diaconis and I. M. Isaacs, Supercharacters and superclasses for algebra groups, Trans. Amer. Math. Soc., 360 (2008), pp. 2359–2392.
[6] L. Dornhoff, Group representation theory. Part A: Ordinary representation theory, vol. 7 of Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1971.
[7] A. Hendrickson, Supercharacter theories of finite cyclic groups, PhD thesis, Department of Mathematics, University of Wisconsin, 2008.
[8] A. O. F. Hendrickson, Supercharacter theory constructions corresponding to Schur ring products, Comm. Algebra, 40 (2012), pp. 4420–4438.
[9] G. James and M. Liebeck, Representations and characters of groups, Cambridge University Press, New York, second ed., 2001.