Sharp Characters Whose Values at Non-identity Elements Are 0 and a Family of Algebraic Conjugates
✍ Scribed by M. Kiyota; S. Nozawa
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 356 KB
- Volume
- 161
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Cameron and Kiyota [J. Algebra 115 (1988), 125-143] posed the problem of determining all the (L)-sharp pairs ((G, \chi)) for a given set (L), and they conjectured that (G) is dihedral of twice odd prime order if (L) is the set ({0} \cup L^{\prime}), where (L^{\prime}) is a family of algebraic conjugates. In their paper and that of S. Nozawa [Tsukuba J. Math. 16 (1992), 269-277] this conjecture is proved to be true under one of the following conditions: (1) (\chi(1)) is coprime to (f_{L}(n) ;(2)\left|L^{\prime}\right|=2 ;(3) \chi) is irreducible. We can now show that this conjecture is true without any additional conditions. 1993 Academic Press, Inc