Notations
- $\le$ is used for subgroup
- $G = \langle A \rangle $ means group $G$ is generated by set $A$
- $P$ means polynomial time in input size.
- $\Omega = \{1,2,3,\cdots,n\}$ is a input domain
- Sym($\Omega$) means symmetric group on $\Omega$
Given: $G = \langle A \rangle, H = \langle B \rangle \le \text{Sym}(\Omega)$, where $G$ normalizes $H$.
Find : $C_G(H) = \{g \in G \mid gh =hg, \forall h \in H\}$
Question : Is it in $P$? Give an polynomial time algorithm if answer is yes. I know that If we drop the normal condition from the above problem then problem will not be in $P$. Also note that computing normaliser of subgroup $H$ is in P.
