TITLE:
Character Products, and Balanced Sets Associated with Group Schemes
ABSTARACT:
Let Irr(G) be the set of absolutely irreducible ordinary characters of
a finite group G. Let f be a faithful character in Irr(G).
If f2 = 1 + mg for some positive integer m and an irreducible character g in Irr(G), then
f(1) = 2, |Z(G)| = 2 and G/Z(G) is isomorphic to A4, S4, or A5.
This gives a classification of a certain class of balanced sets
associated with group association schemes.
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