Related papers: Abelian subgroups of \Out(F_n)

We classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.

We study groups having the property that every non-abelian subgroup contains its centralizer. We describe various classes of infinite groups in this class, and address a problem of Berkovich regarding the classification of finite $p$-groups…

We use the abelian approximation for the bootstrap category of filtered C*-algebras to define a sensible notion of support for its objects. As a consequence, we provide a full classification of localizing subcategories in terms of a product…

In this note we give a new proof of the fact that an elementary subgroup (in the sense of first-order theory) of a non abelian free group $\mathbb{F}$ must be a free factor. The proof is based on definability of orbits of elements of under…

Let F_n be the free group of rank n and let Aut^+(F_n) be its special automorphism group. For an epimorphism pi : F_n -> G of the free group F_n onto a finite group G we call Gamma^+(G,pi) = {f in Aut^+(F_n) | pi*f = pi} the standard…

In this paper, we classify irreducible representations of affine group superschemes over fields $F$ of characteristic not two in terms of those over a separable closure $F^{\mathrm{sep}}$ and their Galois twists. We also compute the…

An approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of…

In this paper, we explore the behaviour of the fixed subgroups of endomorphisms of free-abelian times free (FATF) groups. We exhibit an algorithm which, given a finitely generated subgroup $\mathcal{H}$ of a FATF group $\mathcal{G}$,…

We introduce a new class of Abelian groups which lies strictly between the classes of co-Hopfian groups and Dedekind-finite groups, calling these groups {\it Bassian-finite}. We prove the surprising fact that in the torsion case the…

We generalize the hierarchy construction to generic 2+1D topological orders (which can be non-Abelian) by condensing Abelian anyons in one topological order to construct a new one. We show that such construction is reversible and leads to a…

We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of numerical semigroups are defined giving a classification of…

One of the most studied algebraic structures with one operation is the Abelian group, which is defined as a structure whose operation satisfies the associative and commutative properties, has identical element and every element has an…

Using Goursat's lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z_m x Z_n are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the…

The endomorphism ring End(A) of an abelian variety A is an order in a semi-simple algebra over Q. The co-index of End(A) is the index to a maximal order containing it. We show that for abelian varieties of fixed dimension over any…

A connected component of an affine algebraic group is called periodic if all its elements have finite order. We give a characterization of periodic components in terms of automorphisms with finite number of fixed points. It is also…

We show that any compact group can be realized as the outer automorphism group of a factor of type II_1. This has been proved in the abelian case by Ioana, Peterson and Popa applying Popa's deformation/rigidity techniques to amalgamated…

The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups…

This is the second installment of an exposition of an ACL2 formalization of finite group theory. The first, which was presented at the 2022 ACL2 workshop, covered groups and subgroups, cosets, normal subgroups, and quotient groups,…

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

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…