Characters of finite quasigroups. V: Linear characters (Q1822637)

[Part IV, cf. ibid. 10, No.3, 257-263 (1989; Zbl 0669.20053.] Aspects of the structure of quasigroups with a unique non-linear basic character are investigated. For example, in Section 4 it is shown that the linear basic characters of a general quasigroup are well behaved under multiplication. They form an abelian group which then acts on the remaining basic characters. This action extends to give an abelian group of isometries of the space of class functions. In the final Section the authors examine finite, non-empty quasigroups having a unique non-linear basic character.