Abstract
Let G be a finite group, Q a p-subgroup of G and P a Sylow p-subgroup of Let
be a complete discrete valuation ring of characteristic zero with residue class field
of characteristic p > 0. Suppose that the group ring
is of infinite representation type and
is sufficiently large. Let
be a stable Auslander-Reiten component containing a Scott
-lattice S(Q) with vertex Q. Then all the
-lattices in
have P as their vertices. Also, we show that there exists an indecomposable
-lattice L with vertex P such that a kG-module
is Q-projective.
Communicated by J. Zhang
Acknowledgment
The author would like to thank the referee for reading the manuscript carefully.