Local group theory is the study of a finite group 
using the local
subgroups of 
.
It plays a critical role in the classification
theorem of finite groups. Each local subgroup
is an actual subgroup of 
, with multiplication and inversion defined throughout that
subgroup. This differs from the topological notion of
a local group, which permits restricted domains for
its operations and does not require an ambient group.
Local Group Theory
See also
Sylow TheoremsExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Local Group Theory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LocalGroupTheory.html