Nilpotent groups of class two that can appear as central quotient groups
Suppose that H is a finite group in which \(H'/H'\cap Z(H)\) is central and elementary Abelian of order \(p^ n\). Let \(| H/Z_ 2(H)| =p^ m\). It has long been known that if \(n=1\), then \(m=2\). In the present paper, it is shown that if \(n=2\), then \(2<m<6\), and examples are given which show that for p odd, these bounds are sharp. The proof involves the study of vector spaces with two linearly independent alternating forms. An example is given for general n in which \(m=n(n+3)\).
scientific article; zbMATH DE number 4190008