Computing irreducible representations of supersolvable groups

Baum, Ulrich; Clausen, Michael

doi:10.1090/S0025-5718-1994-1226811-6

Computing irreducible representations of supersolvable groups

Authors: Ulrich Baum and Michael Clausen
Journal: Math. Comp. 63 (1994), 351-359
MSC: Primary 20C40; Secondary 20C15, 68Q40
DOI: https://doi.org/10.1090/S0025-5718-1994-1226811-6
MathSciNet review: 1226811
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Recently, it has been shown that the ordinary irreducible representations of a supersolvable group G of order n given by a power-commutator presentation can be constructed in time $O({n^2}\log n)$ . We present an improved algorithm with running time $O(n\log n)$ .

[1] L. Babai and L. Rónyai, Computing irreducible representations of finite groups, Proc. 30th IEEE Sympos. Foundations of Comput. Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 93-98.
[2] Ulrich Baum, Existence and efficient construction of fast Fourier transforms on supersolvable groups, Comput. Complexity 1 (1991), no. 3, 235–256. MR 1165193, https://doi.org/10.1007/BF01200062
[3] Michael Clausen, Fast generalized Fourier transforms, Theoret. Comput. Sci. 67 (1989), no. 1, 55–63. MR 1015084, https://doi.org/10.1016/0304-3975(89)90021-2
[4] A. Fässler and E. Stiefel, Group theoretical methods and their applications, Birkhäuser Boston, Inc., Boston, MA, 1992. Translated from the German by Baoswan Dzung Wong. MR 1158662
[5] C. R. Leedham-Green, A soluble group algorithm, Computational group theory (Durham, 1982) Academic Press, London, 1984, pp. 85–101. MR 760653