Irreducible congruences of prime power degree

Hanneken, C. B.

doi:10.1090/S0002-9947-1971-0274420-9

Irreducible congruences of prime power degree
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by C. B. Hanneken

Trans. Amer. Math. Soc. 153 (1971), 167-179

DOI: https://doi.org/10.1090/S0002-9947-1971-0274420-9

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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.

References

H. R. Brahana, Metabelian groups of order $p^{n+m}$ with commutator subgroups of order $p^m$, Trans. Amer. Math. Soc. 36 (1934), no. 4, 776–792. MR 1501766, DOI 10.1090/S0002-9947-1934-1501766-3
Leonard Eugene Dickson, An invariantive investigation of irreducible binary modular forms, Trans. Amer. Math. Soc. 12 (1911), no. 1, 1–18. MR 1500877, DOI 10.1090/S0002-9947-1911-1500877-0

Linear groups

C. B. Hanneken, Irreducible congruences over $\textrm {GF}(p)$, Proc. Amer. Math. Soc. 10 (1959), 18–26. MR 105388, DOI 10.1090/S0002-9939-1959-0105388-3

Polynomial subrings of matrices and the linear fractional group