Units of commutative modular group algebras
Let \(FG\) be the group algebra of an abelian \(p\)-group \(G\) over a perfect field \(F\) of characteristic \(p\). The direct factor problem is whether \(G\) is a direct factor of the group V(G) of the normalized units of the unit group \(U(G)\) of \(FG\). This problem has a positive solution if \(V(G)/G\) is simply presented. In the paper under review the author proves that \(V(G)/G\) has a \(\nu\)-basis. Recently the author has established that any abelian \(p\)-group \(A\) with a \(\nu\)-basis such that \(| A| \leq \aleph_ 1\) is simply presented. It is still an open problem whether a group \(A\) with a \(\nu\)-basis is simply presented if \(| A | > \aleph_ 1\).
scientific article; zbMATH DE number 612145
scientific article