Hi,

a module in KG,where G is a p-group and K a field of characteristic p, is called periodic if $ \Omega^{n} M = M $, for a natural n. In general the full subcategory of periodic modules seems to have also wild representation type( http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ijm/1255989005 ). I wonder if there are still some interesting results about periodic modules. So I search for a kind of up-to-date survey paper listing such results. some questions are:

In which dimensions can a module of period n occur?(results like in this paper: http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ijm/1256048241 where it is proven that a power of p divides the dimension)

Which periods can occur in a given group?

Is there any interesting relation of the subcategory of periodic modules and the pure group structure?

Thank you

edit: Another question: Can we give an example of a periodic module in an arbitrary KG?Maybe there is a canonical construction.

edit2: after reading parts of benson im a bit confused.for example in the introduction he says compelextity 1 is equivalent being periodic.But he says something else in a later theorem. Is the following correct?: M has complextity 1 iff

$M_E $ has maximal complextity 1 for an elementar abelian subgroup E of G iff

M is a direct sum of indecomposable periodcis and projectives iff

in the minimal projective resolution the terms have bounded dimension.