This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
View a complete list of subgroup-defining functions OR View a complete list of quotient-defining functions
Suppose is a prime number and is a finite p-group. The Oliver subgroup of , denoted (don't know what that letter actually is) is defined as the unique largest subgroup of such that there exists an ascending series of subgroups of :
- Each is a normal subgroup of .
- We have the condition that for all
where the with occurring times.