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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The number of conjugate sets of irreducible congruences of degree 
belonging to 
, relative to the group 
of linear fractional transformations with coefficients belonging to the same field has been determined for 
. In this paper the irreducible congruences of prime power degree 
, are considered and the number of conjugate sets relative to 
is determined.
- [1] 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, https://doi.org/10.1090/S0002-9947-1934-1501766-3
- [2] Leonard Eugene Dickson, An invariantive investigation of irreducible binary modular forms, Trans. Amer. Math. Soc. 12 (1911), no. 1, 1–18. MR 1500877, https://doi.org/10.1090/S0002-9947-1911-1500877-0
- [3] -, Linear groups, Teubner, Leipzig, 1901.
- [4] C. B. Hanneken, Irreducible congruences over 𝐺𝐹(𝑝), Proc. Amer. Math. Soc. 10 (1959), 18–26. MR 0105388, https://doi.org/10.1090/S0002-9939-1959-0105388-3
- [5] -, Polynomial subrings of matrices and the linear fractional group (submitted).
with commutator subgroup of order 
, Trans. Amer. Math. Soc. 34 (1934), 776-792. 
, Proc. Amer. Math. Soc. 10 (1959), 18-26. MR 21 #4130. Retrieve articles in Transactions of the American Mathematical Society with MSC: 12.20
Retrieve articles in all journals with MSC: 12.20
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1971-0274420-9
Keywords:
Congruences,
linear fractional transformation,
matrix representation,
conjugate set,
transform of a 
ic
congruence,
conjugate under 
,
self-conjugate congruence,
order of a conjugate set,
marks of 
,
complementary function,
normal form of a congruence,
characteristic polynomial,
completely reducible,
normalizer of a subgroup
Article copyright:
© Copyright 1971
American Mathematical Society
