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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Irreducible congruences of prime power degree


Author: C. B. Hanneken
Journal: Trans. Amer. Math. Soc. 153 (1971), 167-179
MSC: Primary 12.20
DOI: https://doi.org/10.1090/S0002-9947-1971-0274420-9
MathSciNet review: 0274420
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0274420-9
Keywords: Congruences, linear fractional transformation, matrix representation, conjugate set, transform of a $ {q^\alpha } -$   ic$ $ congruence, conjugate under $ G$, self-conjugate congruence, order of a conjugate set, marks of $ GF({p^{{q^r}}})$, complementary function, normal form of a congruence, characteristic polynomial, completely reducible, normalizer of a subgroup
Article copyright: © Copyright 1971 American Mathematical Society