相关论文: Stable super summit sets in Garside groups

Let G be a finite solvable permutation group. Then modulo a possibly trivial normal elementary abelian 3-subgroup, some set-stabilizer in G is a 2-group.

This paper has been withdrawn by the authors due to an error in the proof of Lemma 3.9. The correct proof of global stability is given in arXiv:1101.5177

We study stability of metric approximations of countable groups with respect to groups endowed with ultrametrics, the main case study being a $p$-adic analogue of Ulam stability, where we take $GL_n(\mathbb{Z}_p)$ as approximating groups…

We give a positive answer to the question of Shkarin (\emph{On universal abelian topological groups}, Mat. Sb. 190 (1999), no. 7, 127-144) whether there exists a metrically universal abelian separable group equipped with invariant metric.…

We introduce a relaxation of stability, called almost sure stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a non-standard finite group. We show that almost sure stability satisfies a stationarity principle…

A plea to open again the building site of finite simple groups in order to include finite simple hypergroups.

In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…

We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace the well known cycling and decycling operations. Cyclic sliding appears to be a more natural choice,…

This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2073.

In this paper, I survey frame starters, as well as orthogonal and strong frame starters, in abelian groups. I mainly recall and re-examine existence and nonexistence results, but I will prove some new results as well.

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…

In the paper we find new inequalities involving the intersections $A\cap (A-x)$ of shifts of some subset $A$ from an abelian group. We apply the inequalities to obtain new upper bounds for the additive energy of multiplicative subgroups and…

In recent years, there has been a considerable amount of interest in stability of equations and their corresponding groups. Here, we initiate the systematic study of the quantitative aspect of this theory. We develop a novel method,…

This paper has been withdrawn by the author due to that the main results and approaches are closedly parallel to the ones in Lie algebra case.

We consider semi-continuity of certain dimensions on group schemes.

This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0507018), in a clearer way.

The cycling operation endows the super summit set $S_x$ of any element $x$ of a Garside group $G$ with the structure of a directed graph $\Gamma_x$. We establish that the subset $U_x$ of $S_x$ consisting of the circuits of $\Gamma_x$ can be…

A recent result of Balandraud shows that for every subset S of an abelian group G, there exists a non trivial subgroup H such that |TS| <= |T|+|S|-2 holds only if the stabilizer of TS contains H. Notice that Kneser's Theorem says only that…

We show that the geometric realisation of the poset of proper parabolic subgroups of a large-type Artin group has a systolic geometry. We use this geometry to show that the set of parabolic subgroups of a large-type Artin group is stable…

A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(\pi,1)s for Garside groups. This construction shows that the (co)homology of any…