P-group generation algorithm

In mathematics, specifically group theory, finite groups of prime power order ${\displaystyle p^{n}}$, for a fixed prime number ${\displaystyle p}$ and varying integer exponents ${\displaystyle n\geq 0}$, are briefly called finite p-groups.

The p-group generation algorithm by M. F. Newman and E. A. O'Brien is a recursive process for constructing the descendant tree of an assigned finite p-group which is taken as the root of the tree.