On normalized integral table algebras generated by a non-real faithful element of degree 2 with p linear elements

Abstract

In 1995, Blau completely classified the integral table algebras generated by a faithful element of degree 2, all of whose linear basis elements having degrees a power of 2 are equal to 1. By this classification, one can get that the normalized integral table algebra having exactly one linear element and generated by a faithful non-real element of degree 2 is exactly (Ch(SL(2,5)),Irr(SL(2,5))). In this paper, we investigate normalized integral table algebras having more than one linear elements. We once classified normalized integral table algebra with exactly 2 linear elements (see Li and Chen, 2020 [10]). Here we continue this topic and obtain the classification of normalized table algebra (A,B) generated by a faithful non-real element of degree 2 and |L(B)|=p, where p≥3 is a prime.