Papers › Classifying finite monomial linear groups of prime degree in characteristic zero
Classifying finite monomial linear groups of prime degree in characteristic zero
Z. Bácskai, D. L. Flannery, E. A. O'Brien
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Let p be a prime and let ℂ be the complex field. We explicitly classify the finite solvable irreducible monomial subgroups of GL(p,ℂ) up to conjugacy. That is, we give a complete and irredundant list of GL(p,ℂ)-conjugacy class representatives as generating sets of monomial matrices. Copious structural information about non-solvable finite irreducible monomial subgroups of GL(p,ℂ) is also proved, enabling a classification of all such groups bar one family. We explain the obstacles in that exceptional case. For p≤3, we classify all finite irreducible subgroups of GL(p,ℂ). Our classifications are available publicly in Magma.
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