Constructive Representation Theoretic Methods and Non-Abelian Difference Sets
The historical development of a mathematical subject has often begun with the commutative case and then built on this case to unravel the non-commutative. Although the role of non-abelian groups in algebraic combinatorics and finite geometry goes back at least to Dickson (1901), genuinely non-abelian difference sets have only appeared in the last few years, see Liebler and Smith (1993), Smith (1995).
KeywordsGroup Ring Homomorphic Image Permutation Representation Galois Ring Principal Ideal Domain
Unable to display preview. Download preview PDF.
- Assmus, E.F.Jr. and Key, J.D. (1992) Designs and Their Codes, Cambridge University Press.Google Scholar
- Curtis, C.W. and Reiner, I. (1966) Representation Theory of Finite Groups and Associative Algebras, J. Wiley, New York.Google Scholar
- Dickson, L.E. (1901) Linear Groups with an Exposition of the Galois Field Theory, Teubner, Leipzig (reprint Dover, New York 1958).Google Scholar
- Frobenius, F.G. (1968) Gesammelte Abhandlungen 3, Springer, Berlin.Google Scholar
- Jungnickel, D. and Pott, A. (1999) Difference sets: an introduction, the volume.Google Scholar
- Liebler, R.A. and Smith, K.W. (1993) On difference sets in certain 2-groups, in D. Jungnickel (ed.), Coding Theory, Design Theory,Group Theory: Proceedings of the Marshall Hall Conference, John Wiley & Sons, New York.Google Scholar