We describe two algorithms for finding representatives of the nilpotent orbits of a θ-group. The algorithms have been implemented in the computer algebra system GAP (inside the package SLA). We comment on their performance, and we apply the algorithms to obtain lists of N-regular automorphisms of simple Lie algebras of exceptional type.

We study the normal bundles of exceptional sets isolated simple small singularities in higher dimension when Picard group set is $\mathbb{Z}$ and bundle it has some good filtration. In particular, for a projective space with split bundle, we generalized Nakayama Ando's results to dimension. Moreover, also generalize Laufer's rationality embedding

vasil'ev posed problem 16.26 in [the kourovka notebook: unsolved problems in group theory, 16th ed.,sobolev inst. math., novosibirsk (2006).] as follows:does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? conjecture: $k = 5$.in [zvezdina, on nonabelian simple groups having the same prime gr...

Let X be a compact, connected Riemann surface of genus g, and let ρ : X → P (C) be a covering map of degree N . Then the monodromy group Mon(X, ρ) acts transitively on the fibre of a generic point. Such a group has genus g. We are concerned with the following question. Given an abstract finite group G and a non-negative integer g, does G arise as a monodromy group of genus g? The focus in the p...

Let be a nite dimensional hereditary algebra over a nite eld k; H(() and C(() be respectively the Hall algebra and the composition algebra of ; P be the isomorphism classes of nite dimensional-modules and I the isomorphism classes of simple-modules. We deene and , 2 P, to be the right and left derivations of H(() respectively. By using these derivations and the action of the braid group on the ...