A local subgroup of a finite group 
is a normalizer 
, where 
is a nontrivial subgroup whose
group order is a power of
a prime number 
(Aschbacher 2004, p. 738). The subgroup 
need not be a Sylow
p-subgroup.
A local subgroup inherits the fully defined group operation of 
.
By contrast, a local group permits multiplication
and inversion on restricted domains and need not be a subgroup
of an ambient group.
