Splitting of the Main Problem into Four Sub-cases
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In this chapter we collect all necessary definitions and basic facts about Normalized Integral Table Algebras. In this chapter the case (4) is settled provided that the number of constituents in b 3 b 8 is not four. It is shown that under this assumption there are only two NITAs of dimensions 22 and 32. None of them is induced from a group. The case when the number of constituents in b 3 b 8 is four is still open. It is also shown that in the case (3) b 3 b 8 contains exactly three constituents of degrees 6, 10, and 15. It is proved that if the constituent of degree 10 is real, then (A,B)≅ x (CH(PSL(2,7),Irr(PSL(2,7))).
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