Classifying finite monomial linear groups of prime degree in characteristic zero

@article{Bacskai2021ClassifyingFM,
  title={Classifying finite monomial linear groups of prime degree in characteristic zero},
  author={Z. B'acskai and Dane L. Flannery and Eamonn A. O'Brien},
  journal={International Journal of Algebra and Computation},
  year={2021}
}
Let [Formula: see text] be a prime and let [Formula: see text] be the complex field. We explicitly classify the finite solvable irreducible monomial subgroups of [Formula: see text] up to conjugacy. That is, we give a complete and irredundant list of [Formula: see text]-conjugacy class representatives as generating sets of monomial matrices. Copious structural information about non-solvable finite irreducible monomial subgroups of [Formula: see text] is also proved, enabling a classification of… Expand

Tables from this paper

References

SHOWING 1-10 OF 41 REFERENCES
Finite irreducible monomial groups of small prime degree
We present a classification of the finite irreducible complex monomial groups of degree p, where p = 2,3,5,7,11. This is done by giving a family of groups indexed by countably many nonnegativeExpand
Finite collineation groups
  • University of Chicago Press, Chicago,
  • 1917
REPRESENTATION THEORY FOR FINITE GROUPS
We cover some of the foundational results of representation theory including Maschke’s Theorem, Schur’s Lemma, and the Schur Orthogonality Relations. We consider character theory, constructions ofExpand
Computing Projective Indecomposable Modules and Higher Cohomology Groups
We describe the theory and implementation in Magma of algorithms to compute the projective indecomposable KG-modules for finite groups G and finite fields K. We describe also how they may be usedExpand
Recognizing finite matrix groups over infinite fields
TLDR
An algorithm is presented that, given such a finite group as input, in practice successfully constructs an isomorphic copy over a finite field, and uses this copy to investigate the [email protected]?s structure. Expand
The Primitive Permutation Groups of Degree Less Than 4096
In this article we use the Classification of the Finite Simple Groups, the O'Nan–Scott Theorem, and Aschbacher's theorem to classify the primitive permutation groups of degree less than 4096. TheExpand
FOR FINITE GROUPS
Let Q2s be the unique unramifed extension of the two-adic field Q2 of the degree s. Let R be the ring of integers in Q2s Let G be a simply connected Chevalley group corresponding to an irreducibleExpand
MATRIX GROUPS
This paper will be a brief introduction to various groups of matrices and their algebraic, analytic, and topological properties. We consider curves in matrix groups and use them to define theExpand
Linear Groups of Small Degree over Finite Fields
For n = 2,3 and finite field 𝔼 of characteristic greater than n, we provide a complete and irredundant list of soluble irreducible subgroups of GL(n,𝔼). The insoluble irreducible subgroups ofExpand
...
1
2
3
4
5
...