Abstract :
By results of Boltje and K¨ulshammer, if a source algebra A of a
principal p-block of a finite group with a defect group P with inertial quotient
E is a depth two extension of the group algebra of P, then A is isomorphic
to a twisted group algebra of the group P o E. We show in this note that
this is true for arbitrary blocks. We observe further that the results of Boltje
and K¨ulshammer imply that A is a depth two extension of its hyperfocal
subalgebra, with a criterion for when this is a depth one extension. By a
result of Watanabe, this criterion is satisfied if the defect groups are abelian
