5) linear simple algebraic groups 单线性代数群6) absolutely simple algebraic group 绝对单代数群补充资料:殆素数 殆素数 almost - prime number 殆紊数1 alnl砚一prime num加r;朋m盯脚Cr倪,IIc几o] 能表示为下列形式的自然数n: n=PI“’P尸,其中p‘是素数,k)1是常数.素数是殆素数当k=l时的...
We show that the isomorphism theorems from abstract group theory have meaningful analogs for these groups and we establish a Jordan–Hlder type theorem that allows us to decompose any affine difference algebraic group into almost-simple affine difference algebraic groups. We also characterize almost-...
denote a simple algebraic group of adjoint type over an algebraically closed field of characteristic 0, and let \(h_{0}\) be a finite subgroup of \(\mathbf {x}_{0}\) such that \(o_{p}(h_{0})=1\) . if \(\mathbf {x}_{p}\) denotes a simple algebraic group of the same ...
Let g be the Lie algebra of a semi-simple algebraic group G over an algebraically closed field k of characteristic p>0. In the first part of this paper we study the structure of g, and focus on the deviations from the characteristic 0 case. In the second part we determine, for almost...
The main tools include recent work on bases for actions of simple algebraic groups, together with probabilistic methods and improved fixed point ratio estimates for exceptional groups of Lie type.doi:10.1016/j.jalgebra.2018.08.032Burness, Timothy C...
D Leemans,J Moerenhout - 《Journal of Algebraic Combinatorics》 被引量: 2发表: 2016年 Genus One Almost Simple Groups of Lie Rank Two In this paper, we assume that G is a finite group with socle PSL(3, q) and G acts on the projective points of 2-dimensional projective geometry PG(2...
It is a classic result that PSLn(F(k)) is simple unless n=2 and |F(k)|=2,3. In these examples the groups G are amenable since they are locally finite. Example 2.14 Recall that a group is called residually finite if its points are separated by the homomorphisms into finite groups....
Real conjugacy classes in algebraic groups and finite groups of Lie type We recall that an element of a group G is said to be 'real' if it is conjugate to its inverse. A conjugacy class of G is said to be real if it consists of ... PH Tiep,AE Zalesski - 《Journal of Group ...
The reason is that there is no simple criterion for the existence of a lattice in a connected and simply-connected solvable Lie group. We consider the question of existence of lattices in solvable Lie groups up to dimension six and examine whether the corresponding solvmanifolds are formal, ...
Guillemin, V., Sternberg, S.: Geometric quantization and multiplicities of group representations. Invent. Math. 67(3), 515–538 (1982) Article MathSciNet Google Scholar Harish-Chandra.: Invariant differential operators and distributions on a semi-simple Lie algebra. Amer. J. Math. 86, 534–...