Sydney University Algebra Seminar

    University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Bettina Eick
    Universität Braunschweig

    Classifying p-groups by coclass.

    Friday 15th March, 12-1pm, Carslaw 373.

    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.