Related papers: Elementary abelian 2 subgroups of compact Lie grou…

We calssify actions of discrete abelian groups on some inclusions of von Neumann algebras, up to cocycle conjugacy. As an application, we classify actions of compact abelian groups on the inclusions of AFD factors of type II_1 with index…

We prove that the lattice of normal subgroups of ultraproducts of compact simple non-abelian groups is distributive. In the case of ultraproducts of finite simple groups or compact connected simple Lie groups of bounded rank the set of…

In this short note we show that the path-connected component of the identity of the derived subgroup of a compact Lie group consists just of commutators. We also discuss an application of our main result to the homotopy type of the…

We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…

In this note we give a characterization of elementary abelian 2-groups in terms of their maximal sum-free subsets.

We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine…

We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

The lattice of fully invariant subgroups of an abelian $p$--group and the lattice of ideals of its endomorphism ring are classified by systems of cardinal invariants.

Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.

Consider unbounded reduced Abelian p-groups (p > 2) A and A'. In this paper, we prove that if the automorphism groups Aut A and Aut A' are elementary equivalent then the groups A and A' are equivalent in the second order logic bounded by…

We classify, up to conjugacy, the subgroups of the Cremona group isomorphic to (Z/p)^r, where p is prime and r is maximal.

In this paper, we will show that nonabelian simple classical groups of Lie type are uniquely determined by the structure of their complex group algebras.

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…

Let A be the classifying space of an abelian p-torsion group. We compute A-cellular approximations (in the sense of Chach\'olski and Farjoun) of classifying spaces of p-local compact groups, with special emphasis in the cases which arise…

Let $(\mathfrak{g},[p])$ be a restricted Lie algebra over an algebraically closed field $k$ of characteristic $p\!\ge \!3$. Motivated by the behavior of geometric invariants of the so-called $(\mathfrak{g},[p])$-modules of constant $j$-rank…

We show that a minimal ideal of a finite-dimensional Lie algebra is either simple or abelian.

Given a prime power $p^d$ with $p$ a prime and $d$ a positive integer, we classify the finite groups $G$ with $p^{2d}$ dividing $|G|$ in which all subgroups of order $p^d$ are complemented and the finite groups $G$ having a normal…

Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper…

The number of maximal abelian subgroups of a finite p-group is shown to be congruent to 1 modulo p.