# Is Normal centralizer problem in P? [closed]

Notations

1. $\le$ is used for subgroup
2. $G = \langle A \rangle$ means group $G$ is generated by set $A$
3. $P$ means polynomial time in input size.
4. $\Omega = \{1,2,3,\cdots,n\}$ is a input domain
5. 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.

• How are elements of A represented? ​ ​ – user6973 Jan 17 '18 at 16:18
• Now posted also on MathOverflow: Is the Normal centralizer problem in P? – Martin Jan 18 '18 at 14:55