LAUSR

ABSTRACT Let p be a prime, G a finite group, and r≥1. We say a p-block B with defect group D of G is r-small if . In this paper, we show that almost all simple groups have r-small p-blocks, and we explicitly construct them for An and Sn for all primes p. Of course, it is known that for p≥5 that An has a block of defect zero, but little is known about specifically constructing such blocks. Here, however, our explicit construction of r-small p-blocks allows us to construct certain oddly behaved embeddings of q-blocks into p-blocks, where q is a prime distinct from p.