Algebra Seminar

The coclass of a finite p-group G is defined by cc(G) = n - c where |G| = pⁿ and c is the nilpotency class of G. The finite p-groups with coclass r can be sorted into trees: each group of order pⁿ and coclass r corresponds to a node at level n and there is an edge between G and H if G/N \cong H for some N \unlhd G with |N| = p

A famous theorem in the theory of finite p-groups states that there are only finitely many infinite branches in the trees of groups of coclass r. The infinite branches in these trees can in some sense be described by extension of uniserial space groups. This talk contains an investigation of the structure of such uniserial space groups. Based on this a method is introduced to construct such groups and thus the coclass trees for small values of r and p.