On the Endomorphism Semigroups of Extra-special $p$-groups and Automorphism Orbits

C P Anil Kumar, Soham Swadhin Pradhan

For an odd prime $p$ and a positive integer $n$, it is well known that there are two types of extra-special $p$-groups of order $p^{2n+1}$, first one is the Heisenberg group which…