We show that a complete arc K in the projective plane PG(2, q) admitting a transitive primitive group of projective transformations is either a cyclic arc of prime order or a known arc. If the completeness assumption is dropped, then K has either an affine primitive group, or K is contained in an explicit list. In order to find these primitive arcs, it is necessary to determine all complete k-a...

In earlier work we gave a characterisation of pregeometries which are ‘basic’ (that is, admit no ‘non-degenerate’ quotients) relative to two different kinds of quotient operation, namely taking imprimitive quotients and normal quotients. Each basic geometry was shown to involve a faithful group action, which is primitive or quasiprimitive, respectively, on the set of elements of each type. For ...

primitive neuroectodermal tumors of the kidney are rare tumors representing about 1% of all sarcomas. extraskeletal primitive neuroectodermal tumors may be found in the genitourinary tract, the testes, ovaries, uterus, or pancreas. renal primitive neuroec- todermal tumors are frequently aggressive and almost 30% of all newly diagnosed cases present with distant metastases. surgical intervention...

1.1. Aschbacher-Scott Program. Primitive permutation groups have been studied since Galois and Jordan and have applications in many different areas. If Γ is a transitive permutation group with a point stabilizer M then Γ is primitive if and only if M < Γ is a maximal subgroup. So studying primitive permutation groups is equivalent to studying maximal subgroups. In most problems involving a fini...

A partial linear space is a pair $(\mathcal{P},\mathcal{L})$ where $\mathcal{P}$ non-empty set of points and $\mathcal{L}$ collection subsets called lines such that any two distinct are contained in at most one line, every line contains least points. proper when it not or graph. group automorphisms $G$ acts transitively on ordered pairs collinear non-collinear precisely transitive rank 3 In thi...

Let g be a complex simple Lie algebra of type B2 and q be a non-zero complex number which is not a root of unity. In the classical case, a theorem of Dixmier asserts that the simple factor algebras of Gelfand-Kirillov dimension 2 of the positive part U(g) of the enveloping algebra of g are isomorphic to the first Weyl algebra. In order to obtain some new quantized analogues of the first Weyl al...

In a previous paper, we had proved that the permutation group generated by the round functions of an AES-like cipher is primitive. Here we apply the O’Nan Scott classification of primitive groups to prove that this group is the alternating or the symmetric group.