A unit group in a character ring of an alternating group. II
This paper is a continuation of part I [ibid. 20, No. 3, 549-558 (1991)] in which the author showed that the factor group \(U(R(A_ n))/\{\pm 1\}\) is a free abelian group of rank \(c(n)\) [see the preceding review Zbl 0814.20007 for the notations]. In the present paper, the author constructs \(c(n)\) elements \(\psi_ 1,\dots,\psi_{c(n)}\) in \(U(R(A_ n))\) such that the subgroup of \(U(R(A_ n))\) generated by these elements has rank \(c(n)\) and contains \(\{\psi^ 2 \mid \psi \in U(R(A_ n))\}\) as is subset. The author also gives a necessary and sufficient condition on an element \(\psi \in U(R(A_ n))\) to be the difference of two irreducible complex characters of \(A_ n\).
scientific article; zbMATH DE number 165207