Omega subgroups not are prehomomorph-contained
This article gives the statement, and possibly proof, of the fact that for a group, the subgroup obtained by applying a given subgroup-defining function (i.e., omega subgroups of group of prime power order) does not always satisfy a particular subgroup property (i.e., prehomomorph-contained subgroup)
View subgroup property satisfactions for subgroup-defining functions View subgroup property dissatisfactions for subgroup-defining functions
It is possible to have a group of prime power order (i.e., a finite -group for some prime number ), a subgroup of , and a surjective homomorphism , such that is not contained in .
Analogous examples can be constructed for for any .
Let be the quaternion group of order eight and be the cyclic group of order two. Define: