Schur multiplicators of finite \(p\)-groups with fixed coclass. (Q948879)

The author investigates the Schur multiplicators \(M(G)\) of finite \(p\)-groups \(G\) using the coclass as primary invariant (the coclass of a group of order \(p^n\) and class \(c\) is \(n-c\)). For \(p>2\), she proves that there are at most finitely many \(p\)-groups \(G\) of coclass \(r\) with \(|M(G)|\leq s\) for every \(r\) and \(s\). This is not true for \(p=2\). Infinite series of 2-groups \(G\) with coclass \(r\) and trivial Schur multiplicator are constructed. Coclass theory is used to further investigate the Schur multiplicators of 2-groups of coclass \(r\).