Glasnik Matematicki, Vol. 45, No.2 (2010), 407-413.

ON SQUARES OF IRREDUCIBLE CHARACTERS

Emmanuel Zhmud

Abstract.   We study the finite groups G with a faithful irreducible character whose square is a linear combination of algebraically conjugate irreducible characters of G. In conclusion, we offer another proof of one theorem of Isaacs-Zisser.

2000 Mathematics Subject Classification.   20C15.

Key words and phrases.   Generalized character, algebraic conjugate, irreducible characters, quasikernel, exterior power.

DOI: 10.3336/gm.45.2.08

References:

1. Y. Berkovich and E. Zhmud, Characters of Finite Groups, Parts 1, 2, AMS, Providence, 1998.
   MathSciNet     MathSciNet    

2. H. Blau and D. Chillag, On powers of characters and powers of conjugacy classes of a finite group, Proc. Amer. Math. Soc. 98 (1986), 7-10.
   MathSciNet     CrossRef

3. I. M. Isaacs and I. Zisser, Squares of characters with few irreducible constituents in finite groups, Arch. Math. (Basel) 63 (1994), 197-207.
   MathSciNet     CrossRef