  In this PhD thesis we discuss methods of recognizing finite groups by the
structure of normalizers of certain 3-subgroups. We explain a method for
characterizing groups using character theoretic and block theoretic methods and
we use these methods to characterize $\alt(9)$. Furthermore, we describe a
particular hypothesis related to the 3-local structure of finite groups of
local characteristic 3 and characterize two almost simple proper extensions of
$\Omega^+_8(2)$ as examples of the local approach to group recognition. We also
give a 3-local characterization of the sporadic simple group $\HN$ using local
methods whilst applying a character theoretic result.
