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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On open subgroups of p-adic algebraic groups
p-adic 代数群 开子群
2023/5/5
In this talk, I will breifly introduce the p-aidc number, p-aidc manifolds, p-adic algebraic groups and p-aidc definable groups. Using an elementary method, I will show that every open subgroup of a c...
On partially conjugate-permutable subgroups of finite groups
conjugate-permutable subgroups of finite groups Group Theory
2012/6/12
Let $R$ be a subset of a group $G$. We call a subgroup $H$ of $G$ the $R$-conjugate-permutable subgroup of $G$, if $HH^{x}=H^{x}H$ for all $x\in R$. This concept is a generalization of conjugate-permu...
The normalizers of solvable spherical subgroups
Algebraic group spherical subgroup solvable subgroup normalizer
2011/9/21
Abstract: For an arbitrary connected solvable spherical subgroup H of a connected semisimple algebraic group G we compute the group N_G(H), the normalizer of H in G. Thereby we complete a classificati...
A characterization of normal subgroups via n-closed sets
subgroup normal subgroup left coset n-closed set
2011/9/20
Abstract: Let (G, *) be a semigroup, D subset of G, and n >= 2 be an integer. We say that (D, *) is an n-closed subset of G if a_1* ... *a_n in D for every a_1, ..., a_n in D. Hence every closed set i...
The automorphism group of Thompson's group F: subgroups and metric properties
automorphism group Thompson's group F subgroups and metric properties
2011/9/16
Abstract: We describe some of the geometric properties of the automorphism group Aut(F) of Thompson's group F. We give realizations of Aut(F) geometrically via periodic tree pair diagrams, which lead ...
Verbal subgroups of hyperbolic groups have infinite width
Verbal subgroups hyperbolic groups Group Theory
2011/9/14
Abstract: Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subg...
Fixed points subgroups $G^{\sigma,\sigma'}$ by two involutive automorphisms $\sigma$, $\sigma'$ of exceptional compact Lie group $G$, Part II, $G = E_8$
Exceptional Lie group Symmetric space
2011/2/21
For the simply connected compact exceptional Lie group E8, we determine the structure of subgroup (E8).
Fixed points subgroups by two involutive automorphisms $\sigma, \gamma$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$
Fixed points subgroups by two involutive automorphisms $\sigma \gamma$ of compact exceptional Lie groups $F_4, E_6$ $E_7$
2011/2/21
For simply connected compact exceptional Lie groups G = F4,E6 and E7, we consider two involutions σ, γ and determine the group structure of subgroups G,of G which are the intersection G ∩ G of the ...
Subgroups of isometries of Urysohn-Katetov metric spaces of uncountable density
Subgroups of isometries of Urysohn-Katetov metric uncountable density
2011/1/18
According to Katˇetov (1988), for every infinite cardinal m satisfying m n ≤ m for all
n < m, there exists a unique m-homogeneous universal metric space Um of weight m.
Smooth Lie group actions are parametrized diffeological subgroups
Smooth Lie group actions parametrized diffeological subgroups
2011/1/17
We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset
diffeology of the functio...
Loop subgroups of F_r and the image of their stabilizer subgroups in GL_r(Z)
Loop subgroups of F_r image of their stabilizer subgroups
2011/1/21
For a representative class of subgroups of Fr , the image of their stabilizer subgroup under
the action of Aut(Fr ) in GLr (Z) is calculated.
Let p > 2 be a rational prime and K/Qp be an extension of complete discrete valuation fields. Let G be a truncated Barsotti-Tate group of level n, height h and dimension d over OK with 0 < d < h.In th...
Combinatorial Methods for Detecting Surface Subgroups in Right-Angled Artin Groups
Combinatorial Methods Surface Subgroups Right-Angled Artin Groups
2011/2/23
We give a short proof of the following theorem of Sang-hyun Kim:if A() is a right-angled Artin group with de ning graph , then A() contains a hyperbolic surface subgroup ...
We study the subgroup structure of the \'etale fundamental group $\Pi$ of a projective curve over an algebraically closed field of characteristic 0. We obtain an analog of the diamond theorem for $\P...
Lipschitz retraction and distortion for subgroups of Out(F_n)
Lipschitz retraction distortion subgroups of Out(F_n)
2010/12/13
Given a finitely generated group G, a finitely generated subgroup H is undistorted in G if the inclusion map H →֒ G is a quasi-isometric embedding with respect to word metrics. Nondistortion may...