Related papers: Groups of Intermediate Growth: an Introduction for…
An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in arithmetic progressions.
In this paper, we describe the structure of finite groups whose element orders or proper (abelian) subgroup orders form an arithmetic progression of ratio $r\geq 2$. This extends the case $r=1$ studied in previous papers \cite{1,8,4}.
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and…
We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on both.
We consider the growth, order, and finiteness problems for automaton (semi)groups. We propose new implementations and compare them with the existing ones. As a result of extensive experimentations, we propose some conjectures on the order…
This paper gives asymptotic formulas for the subgroup growth and maximal subgroup growth of all Baumslag-Solitar groups.
The aim of this text is to provide a clear description of the theory of Infra-nilmanifolds and their fundamental groups, the almost-Bieberbach groups. For most of the proofs of the results, we refer to the literature. Nevertheless, at…
This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.
Computations in the cohomology of finite groups.
We show that there exists a finitely generated group of growth ~f for all functions f:\mathbb{R}\rightarrow\mathbb{R} satisfying f(2R) \leq f(R)^{2} \leq f(\eta R) for all R large enough and \eta\approx2.4675 the positive root of…
We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.
This paper aims to introduce a more general definition of quasirandom groups and generalize several well-known results in the literature in this new setting. More precisely, let $G$ be a semi-direct product of groups and $X\subseteq G$, we…
We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…
Mathematical methods of analysis of data and of predicting growth are discussed. The starting point is the analysis of the growth rates, which can be expressed as a function of time or as a function of the size of the growing entity.…
We present the ideas behind an algorithm to compute normalizers of primitive groups with non-regular socle in polynomial time. We highlight a concept we developed called permutation morphisms and present timings for a partial implementation…
We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
The paper is an introduction to intuitionistic mathematics.
We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…