Irreducible congruences over 𝐺𝐹(2)

Hanneken, C. B.

doi:10.1090/S0002-9947-1974-0347782-4

Irreducible congruences over $\textrm {GF}(2)$
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by C. B. Hanneken

Trans. Amer. Math. Soc. 193 (1974), 291-301

DOI: https://doi.org/10.1090/S0002-9947-1974-0347782-4

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Abstract:

In characterizing and determining the number of conjugate sets of irreducible congruences of degree m belonging to $GF(p)$ relative to the group $G(p)$ of linear fractional transformations with coefficients belonging to the same field, the case $p = 2$ has been consistently excluded from considerations. In this paper we consider the special case $p = 2$ and determine the number of conjugate sets of m-ic congruences belonging to $GF(2)$ relative to $G(2)$.

References

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
C. B. Hanneken, Irreducible congruences of prime power degree, Trans. Amer. Math. Soc. 153 (1971), 167–179. MR 274420, DOI 10.1090/S0002-9947-1971-0274420-9