# Pi-series

From Groupprops

## Definition

Let be a finite group and be a set of prime numbers. A -series of is a subnormal series with the property that every factor group of the series is either a -group (all the prime factors of its order are in ) or a -group (none of the prime factors of its order are in ).

If possesses a -series, then is termed a pi-separable group. Two pi-series of particular interest are the upper pi-series and lower pi-series.