Generating wreath products and their augmentation ideals
For a group \(W\), let \(d(W)\) denote the minimum of the cardinalities of the generating sets of \(W\). The author studies \(d(W)\) for the wreath product \(W=H\wr G\) of a group \(H\) and a finite permutation group \(G\). He obtains formulas for \(d(W)\) when \(H\) is a finite soluble group and \(G\) is a transitive permutation group, or \(H\) is a nontrivial abelian group and \(G\) is the symmetric group. In addition, the author studies \(d(I_W)\), where \(d(I_W)\) denotes the minimum number of generators of the augmentation ideal \(I_W\) of the group ring \(ZW\) as a \(ZW\)-module.
scientific article; zbMATH DE number 1115652