منابع مشابه
Imprimitive Permutation Groups
The O’Nan-Scott Theorem together with the Classification of the Finite Simple Groups is a powerful tool that give the structure of all primitive permutation groups, as well as their actions. This has allowed for the solution to many classical problems, and has opened the door to a deeper understanding of imprimitive permutation groups, as primitive permutation groups are the building blocks of ...
متن کاملOn imprimitive rank 3 permutation groups
A classification is given of rank 3 group actions which are quasiprimitive but not primitive. There are two infinite families and a finite number of individual imprimitive examples. When combined with earlier work of Bannai, Kantor, Liebler, Liebeck and Saxl, this yields a classification of all quasiprimitive rank 3 permutation groups. Our classification is achieved by first classifying imprimi...
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In an earlier paper the authors have classified the nonsolvable primitive linear groups of prime degree over C. The present paper deals with the classification of the nonsolvable imprimitive linear groups of prime degree (equivalently, the irreducible monomial groups of prime degree). If G is a monomial group of prime degree r, then there is a projection π of G onto a transitive group H of perm...
متن کاملFusion Algebras for Imprimitive Complex Reflection Groups
We prove that the Fourier matrices for the imprimitive complex reflection groups introduced by Malle in [9] define fusion algebras with not necessarily positive but integer structure constants. Hence they define Z-algebras. As a result, we obtain that all known Fourier matrices belonging to spetses define algebras with integer structure constants.
متن کاملUnipotent Degrees of Imprimitive Complex Reflection Groups
In the representation theory of finite groups of Lie type G(q) the unipotent characters play a fundamental role. Their degrees, seen as polynomials in q, are only dependent on the Weyl group of G(q). G. Lusztig (Astérisque 212 (1993) 191–203) has shown that one can define unipotent degrees for a general finite Coxeter group. In this article we construct, for the two infinite series of n-dimensi...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1904
ISSN: 0002-9327
DOI: 10.2307/2369906