This article is concerned with conjugacy problems arising in homeomorphisms group, Hom(F ), of non-compact subsets F of normed vector spaces E. Given two homeomorphisms f and g in Hom(F ), it is shown how the existence of a conjugacy may be related to the existence of a common generalized eigenfunction of the associated Koopman operators. This common eigenfunction serves to build a topology on ...

Let G be a reductive group over an algebraically closed field whose characteristic is not a bad prime for G. Let w be an elliptic element of the Weyl group which has minimum length in its conjugacy class. We show that there exists a unique unipotent class X in G such that the following holds: if V is the variety of pairs (g,B) where g ∈ X and B is a Borel subgroup such that B, gBg−1 are in rela...

Abstract In this paper, we consider the conjugacy stability property of subgroups and provide effective procedures to solve problem in several classes groups. particular, start with free groups, that is, give an procedure find out if a finitely generated subgroup group is stable. Then further generalize result quasi-convex torsion-free hyperbolic groups limit

Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $sigma^{ast}(G)=2$, a finite simple group $G$ that satisfies the one-p...

FEDERICO SÁNCHEZ-BRINGAS Let I' be a finite subgroup of GL(n, (C) . This subgroup acts on the space of germs of holomorphic vector fields vanishing at the origin in Cn and on the group of germs of holomorphic diffeomorphisms of ((Cn, 0) . We prove a theorem of invariant conjugacy to a normal form and linearization for the subspace of invariant germs of holomorphic vector fields and we give a de...

Valuations on a field K are encoded in the absolute Galois group GK of K: They are in one-to-one correspondence to the conjugacy classes of decomposition subgroups of GK which (apart from few exceptions) can be characterized in group theoretic terms. Roughly speaking decomposition subgroups of GK are maximal subgroups of GK with a Sylow-subgroup containing a non-trivial abelian normal subgroup....

Denote by $B_n$ the set of complex square matrices order $n$, whose Euclidean operator norms are $<1$. Its Shilov boundary is $U(n)$ all unitary matrices. A holomorphic map $B_m\to B_n$ inner if it sends $U(m)$ to $U(n)$. On other hand we consider a group $U(n+mj)$ and its subgroup $U(j)$ embedded in block-diagonal way ($m$ blocks unit block size $n$). For any conjugacy class with respect assig...

Let G be a group and φ an automorphism of G. Two elements x,y are said to φ-twisted conjugate if y=gxφ(g)−1 for some g∈G. A has the R∞-property number conjugacy classes is infinite every In this paper, we prove that big mapping class MCG(S) possesses under suitable conditions on infinite-type surface S. As application, also only it satisfies S∞-property.