On coclass and trivial Schur multiplicator.
Recall, a \(p\)-group of order \(p^n\) and nilpotency class \(c\) has coclass \(r=n-c\). In [J. Algebra 322, No. 3, 741-751 (2009; Zbl 1196.20019)] \textit{B. Eick} conjectures that, for odd \(p\), the order of a \(p\)-group with trivial Schur multiplicator and coclass \(r\) is bounded by a function \(b(r)\) which is independent of \(p\). In the paper under review this conjecture is confirmed for coclass 2. In particular, the author shows that, for odd prime \(p\), a \(p\)-group with coclass 2 and trivial Schur multiplicator has nilpotency class at most 6.
scientific article; zbMATH DE number 5610511