Regular orbits of finite primitive solvable groups, the final classification
نویسندگان
چکیده
Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on vector space V, is not metacyclic. Then always has regular orbit V except for few “small” cases. We completely classify these cases in this paper.
منابع مشابه
Complex Orbits of Solvable Groups
The following structure theorems are proved: An orbit of a real solvable Lie group in projective space that is a complex submanifold is isomorphic to C x (C*)m x Í2 , where Í2 is an open orbit of a real solvable Lie group in a projective rational variety. Also, any homogeneous space of a complex Lie group that is isomorphic to C" can be realized as an orbit in some projective space. As a conseq...
متن کاملClassification of solvable groups with a given property
In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.
متن کاملfinite bci-groups are solvable
let $s$ be a subset of a finite group $g$. the bi-cayley graph ${rm bcay}(g,s)$ of $g$ with respect to $s$ is an undirected graph with vertex set $gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin g, sin s}$. a bi-cayley graph ${rm bcay}(g,s)$ is called a bci-graph if for any bi-cayley graph ${rm bcay}(g,t)$, whenever ${rm bcay}(g,s)cong {rm bcay}(g,t)$ we have $t=gs^alpha$ for some $...
متن کاملGroup Membership for Groups with Primitive Orbits
This paper considers a permutation group G = 〈S〉 of degree n with t orbits such that the action on each orbit is primitive. It presents a O(tn2 logc(n)) time Monte Carlo group membership algorithm for some constant c. The algorithm is notable for its use of a new theorem showing how to find O(t log n) generators in O (̃|S|n) time under a more general form of the above hypotheses. The algorithm r...
متن کاملThe Minimal Base Size of Primitive Solvable Permutation Groups
A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. Answering a question of Pyber, we prove that all primitive solvable permutation groups have a base of size at most four.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2023
ISSN: ['1095-855X', '0747-7171']
DOI: https://doi.org/10.1016/j.jsc.2022.08.019