School of Mathematics and Statistics
Bettina Eick
Universität Braunschweig
Classifying pgroups by coclass.
Friday 15th March, 121pm,
Carslaw 373.
The coclass of a finite pgroup G is defined by
cc(G) = n  c where G = p^{n} and c is the
nilpotency class of G. The finite pgroups with
coclass r can be sorted into trees: each group of order
p^{n} 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 pgroups 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.
