ieja International Electronic Journal of Algebra 1306-6048 Abdullah HARMANCI 10.24330/ieja.440216 Mathematical Sciences Matematik A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP Linckelmann Markus 07 05 2018 24 24 68 72 10 30 2017 Copyright © 2007, International Electronic Journal of Algebra 2007 International Electronic Journal of Algebra

By results of Boltje and Kulshammer, if a source algebra A of aprincipal p-block of a nite group with a defect group P with inertial quotientE is a depth two extension of the group algebra of P, then A is isomorphicto a twisted group algebra of the group P o E. We show in this note thatthis is true for arbitrary blocks. We observe further that the results of Boltjeand Kulshammer imply that A is a depth two extension of its hyperfocalsubalgebra, with a criterion for when this is a depth one extension. By aresult of Watanabe, this criterion is satised if the defect groups are abelian.

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