相关论文: Direct limit groups do not have small subgroups

In this paper we extend the results on controllability of linear systems obtained in "Controllability of linear systems on solvable Lie groups", from solvable Lie groups to Lie groups with finite semisimple center.

We describe finite-dimensional smooth Lie groups over local fields of positive characteristic which do not admit an analytic Lie group structure compatible with the given topological group structure, and C^n-Lie groups without a compatible…

In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these simple groups have infinite $w$-verbal width for all…

In this paper we show that there is an infinite number of finite groups with two relative subgroup commutativity degrees. Also, we indicate a sufficient condition such that a finite group has at least three relative subgroup commutativity…

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…

We initiate the study of some pro-p-groups arising from infinite-dimensional Lie theory. These groups are completions of some subgroups of incomplete Kac-Moody groups over finite fields, with respect to various completions of algebraic or…

We show that an infinite group $G$ definable in a $1$-h-minimal field admits a strictly $K$-differentiable structure with respect to which $G$ is a (weak) Lie group, and show that definable local subgroups sharing the same Lie algebra have…

We show that there is a class of finite groups, the so-called perfect groups, which cannot exhibit anomalies. This implies that all non-Abelian finite simple groups are anomaly-free. On the other hand, non-perfect groups generically suffer…

We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.

We show that for any pair of non-trivial finite groups, their coproduct in the category of finite groups is not representable.

We construct an infinite discrete subgroup of the isometry group of $\mathbb H^3$ with no finite quotients other than the trivial group.

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n \in \mathbb{N}^*\setminus \lbrace 2\rbrace$ and we indicate…

We prove that all finitely generated fully residually free groups (limit groups) have a sequence of finite dimensional unitary representations that `strongly converge' to the regular representation of the group. The corresponding statement…

We prove the conjugacy of Sylow $p$-subgroups of linear pseudofinite groups under the assumption of the existence of a finite Sylow $p$-subgroup. We also give an example of a linear pseudofinite group with non-conjugate Sylow $2$-subgroups.

We are interested in subgroups of the reals that are small in one and large in another sense. We prove that, in ZFC, there exists a non-meager Lebesgue null subgrooup of R, while it isconsistent there there is no non-null meager subgroup of…

We prove that there is a second countable locally compact group that does not embed as a closed subgroup in any compactly generated locally compact group, and discuss various related embedding and non-embedding results.

We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented…

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…

We show that finite quasisimple groups of Lie type in characteristic $p$ with an irreducible representation of prime degree $r$ over a finite field of characteristic $p$ have orders bounded above by a function of $r$, independent of $p$. We…

We introduce the notion of the depth of a finite group $G$, defined as the minimal length of an unrefinable chain of subgroups from $G$ to the trivial subgroup. In this paper we investigate the depth of (non-abelian) finite simple groups.…