Let $p$ be a prime number and $P$ a $p$group.
(1) If $A$ is a maximal Abelian subgroup, what are nice examples where it isn't selfcentralizing?
(2) What if $A$ happens to be normal as well?
Let $p$ be a prime number and $P$ a $p$group. (1) If $A$ is a maximal Abelian subgroup, what are nice examples where it isn't selfcentralizing? (2) What if $A$ happens to be normal as well? 

