Let be a group, and let . The normalizer of in , written , is the set
A subgroup of is said to be self-normalizing if .
is always a subgroup of , as it is the stabilizer of under the action of on the set of all subsets of (or on the set of all subgroups of , if is a subgroup).
If is a subgroup of , then .
If is a subgroup of , then is a normal subgroup of ; in fact, is the largest subgroup of of which is a normal subgroup. In particular, if is a subgroup of , then is normal in if and only if .
|Date of creation||2013-03-22 12:36:53|
|Last modified on||2013-03-22 12:36:53|
|Last modified by||yark (2760)|