Related papers: Subgroups of simple primitive permutation groups d…

We propose an interpretation for the meets and joins in the lattice of experimental propositions of a physical theory, answering a question of Birkhoff and von Neumann in [1]. When the lattice is atomistic, it is isomorphic to the lattice…

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and $*$ the classical involution of $FG$. The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all…

We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a…

Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special…

We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $2^k -1$ for some $k$; or (c) a projective special linear…

We consider three isogeny invariants of abelian varieties over finite fields: the Galois group, Newton polygon, and the angle rank. Motivated by work of Dupuy, Kedlaya, and Zureick-Brown, we define a new invariant called the weighted…

A group $G$ given by a presentation $G = < \mathcal A \| \mathcal R >$ is called weakly finitely presented if every finitely generated subgroup of $G$, generated by (images of) some words in $\mathcal A^{\pm 1}$, is naturally isomorphic to…

Let $p$ be a prime and $F$ be a finite field of characteristic $p$. Suppose that $FG$ is the group algebra of the finite $p$-group $G$ over the field $F$. Let $V(FG)$ denote the group of normalized units in $FG$ and let $V_*(FG)$ denote the…

We define and study quantum permutations of infinite sets. This leads to discrete quantum groups which can be viewed as infinite variants of the quantum permutation groups introduced by Wang. More precisely, the resulting quantum groups…

The space of n (ordered) points on the projective line, modulo automorphisms of the line, is one of the most important and classical examples of an invariant theory quotient, and is one of the first examples given in any course. Generators…

Comparability graphs are graphs which have transitive orientations. The dimension of a poset is the least number of linear orders whose intersection gives this poset. The dimension ${\rm dim}(X)$ of a comparability graph $X$ is the…

The relational complexity of a subgroup $G$ of $\mathrm{Sym}(\Omega)$ is a measure of the way in which the orbits of $G$ on $\Omega^k$ for various $k$ determine the original action of $G$. Very few precise values of relational complexity…

A finite group $G$ is called uniformly semi-rational if there exists an integer $r$ such that the generators of every cyclic sugroup $\langle x \rangle$ of $G$ lie in at most two conjugacy classes, namely $x^G$ or $(x^r)^G$. In this paper,…

The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…

This paper is devoted to a study of the automorphism groups of three series of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over a field of prime characteristic. Our aim is to characterize the connections between…

Let $G$ be a finite non-regular primitive permutation group on a set $\Omega$ with point stabiliser $G_{\alpha}$. Then $G$ is said to be extremely primitive if $G_{\alpha}$ acts primitively on each of its orbits in $\Omega \setminus…

The Gruenberg-Kegel graph $\Gamma(G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $|G|$ and in which two distinct vertices $r$ and $s$ are adjacent if and only if there exists an element of order $rs$…

Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal…

In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order $p^{22}$ tends to infinity with $p$. More precisely, for each prime number $p$ there is a family…

In this article we give an algorithm for determining the generators and relations for the rings of semi-invariant functions on irreducible components of representation spaces for gentle string algebras. These rings of semi-invariants turn…