Nonvanishing Elements in Table Algebras

REFERENCES

• Arad , Z. , Blau , H. I. ( 1991 ). On table algebras and applications to finite group theory . J. Algebra 138 : 137 – 185 .
   Web of Science ®Google Scholar
• Arad , Z. , Fisman , E. , Muzychuk , M. ( 1999 ). Generalized table algebras . Israel J. Math 114 : 29 – 60 .
   Web of Science ®Google Scholar
• Bannai , E. , Ito , I. ( 1984 ). Algebraic Combinatorics I. Association Schemes. Menlo Park: Benjamin/Cummings .
   Google Scholar
• Blau , H. I. ( 2010 ). Decomposition of products in nilpotent table algebras . J. Algebra 323 : 1581 – 1592 .
   Web of Science ®Google Scholar
• Blau , H. I. ( 2009 ). Table algebras . European J. Combin. 30 : 1426 – 1455 .
   Web of Science ®Google Scholar
• Blau , H. I. ( 1995 ). Quotient structures in C-algebras . J. Algebra 175 : 24 – 64 .
   Web of Science ®Google Scholar
• Ya , G. , Berkovich , E. M. ( 1998 ). Zhmud’ Characters of Finite Groups, Part 1 . Providence , Rhode Island : American Mathematical Society .
   Google Scholar
• Blau , H. I. , Zieschang , P. H. ( 2004 ). Sylow theory for table algebras, fusion rule algebras, and hypergroups . J. Algebra 273 : 551 – 570 .
   Web of Science ®Google Scholar
• Chen , G. ( 2010 ). Finite groups and elements where characters vanish . Arch. Math. 94 : 419 – 422 .
   Web of Science ®Google Scholar
• Drobotenko , V. C. ( 1975 ). A characterization of nilpotent groups in the language of characters . Ukrainian Math. J. 27 : 63 – 64 .
   Google Scholar
• Gelaki , S. , Nikshych , D. ( 2008 ). Nilpotent fusion categories . Adv. Math. 217 : 1053 – 1071 .
   Web of Science ®Google Scholar
• Hanaki , A. ( 2008 ). Nilpotent schemes and group-like schemes . J. Combin. Theory Ser. A 115 : 226 – 236 .
   Web of Science ®Google Scholar
• Isaacs , I. M. , Navarro , G. , Wolf , T. R. ( 1999 ). Finite group elements where no irreducible character vanishes . J. Algebra 222 : 413 – 423 .
   Web of Science ®Google Scholar
• Isaacs , I. M. ( 1976 ). Character Theory of Finite Groups . New York , San Francisco, London : Academic Press .
   Google Scholar
• Takegahara , Y. , Yoshida , T. ( 2008 ). Character theoretical aspects of nilpotency class . Comm. Algebra 36 : 2625 – 2637 .
   Web of Science ®Google Scholar
• Xu , B. ( 1995 ). On a class of integral table algebras . J. Algebra 178 : 760 – 781 .
   Web of Science ®Google Scholar
• Zieschang , P.-H. ( 1996 ). An algebraic approach to association schemes . In: Lecture Notes in Math . Vol. 1628 . Berlin : Springer-Verlag .
   Google Scholar
• Communicated by Q. Wu.
   Google Scholar