Normal core of normalizer
This article defines a subgroup operator related to the subgroup property normal subgroup. By subgroup operator is meant an operator that takes as input a subgroup of a group and outputs a subgroup of the same group.
- It is the largest normal subgroup of that normalizes . In other words, it is the largest normal subgroup of contained in the normalizer .
- It is the normal core of the normalizer in .
is contained in the normal core of normalizer of if and only if is a 2-subnormal subgroup of . In this case, if is the normal core of normalizer of , then the ascending chain is the unique fastest ascending subnormal series for in . Further information: 2-subnormal subgroup has a unique fastest ascending subnormal series