On powers of characters and powers of conjugacy classes of a finite group

Authors:
Harvey I. Blau and David Chillag

Journal:
Proc. Amer. Math. Soc. **98** (1986), 7-10

MSC:
Primary 20C15

MathSciNet review:
848863

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Abstract: Two results are proved. The first gives necessary and sufficient conditions for a power of an irreducible character of a finite group to have exactly one irreducible constituent. The other presents necessary and sufficient conditions for a power of a conjugacy class of a finite group to be a single conjugacy class. Examples are given.

**[1]**Z. Arad and M. Herzog (eds.),*Products of conjugacy classes in groups*, Lecture Notes in Mathematics, vol. 1112, Springer-Verlag, Berlin, 1985. MR**783067****[2]**Z. Arad, J. Stavi, and M. Herzog,*Powers and products of conjugacy classes in groups*, Products of conjugacy classes in groups, Lecture Notes in Math., vol. 1112, Springer, Berlin, 1985, pp. 6–51. MR**783068**, 10.1007/BFb0072286**[3]**Zvi Arad, David Chillag, and Gadi Moran,*Groups with a small covering number*, Products of conjugacy classes in groups, Lecture Notes in Math., vol. 1112, Springer, Berlin, 1985, pp. 222–244. MR**783071**, 10.1007/BFb0072289**[4]**Zvi Arad, David Chillag, and Marcel Herzog,*Powers of characters of finite groups*, J. Algebra**103**(1986), no. 1, 241–255. MR**860703**, 10.1016/0021-8693(86)90183-3**[5]**Z. Arad and E. Fisman,*An analogy between products of two conjugacy classes and products of two irreducible characters in finite groups*(submitted to Proc. Edinburgh Math. Soc).**[6]**H. I. Blau,*On tensor products of simple modules for finite group algebras*(in preparation).**[7]**Frank R. DeMeyer and Gerald J. Janusz,*Finite groups with an irreducible representation of large degree*, Math. Z.**108**(1969), 145–153. MR**0237629****[8]**Robert B. Howlett and I. Martin Isaacs,*On groups of central type*, Math. Z.**179**(1982), no. 4, 555–569. MR**652860**, 10.1007/BF01215066**[9]**I. Martin Isaacs,*Character theory of finite groups*, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 69. MR**0460423****[10]**A. Mann,*Products of classes and characters in finite groups*(in preparation).

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0848863-2

Article copyright:
© Copyright 1986
American Mathematical Society