Abstract
The number of conjugate sets of irreducible congruences of degree $m$ belonging to $GF(p),p > 2$, relative to the group $G$ of linear fractional transformations with coefficients belonging to the same field has been determined for $m \leqq 8$. In this paper the irreducible congruences of prime power degree ${q^\alpha },q > 2$, are considered and the number of conjugate sets relative to $G$ is determined.
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