Weight for a finite group
From Groupprops
Definition
Definition with symbols
let be a prime and
a finite group. A weight of
is a pair
such that:
-
is a
-subgroup of
, and in fact,
(viz it is the
-Sylow core of its normalizer
).
-
is an irreducible character of
, the restriction of
to
is trivial, and
belongs to a
-block of
of defect zero.
Equivalence notion
Two weights are said to be equal if their is an inner automorphism of taking one to the other.
Weights for a block
For a
-block of
, the weight is said to eb a
-weight if
where
is the associated block on
.