Related papers: Metabelianisations of finitely presented groups
Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.
We show that a profinite group, in which the centralisers of non-trivial elements are metabelian, is either virtually pro-$p$ or virtually soluble of derived length at most 4. We furthermore show that a prosoluble group, in which the…
We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.
There are various results in the literature which are part of the general philosophy that a finite group for which a certain parameter (for example, the number of conjugacy classes or the maximum number of elements inverted, squared or…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…
We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.
This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…
In this paper, we compute an upper bound for the Dehn function of a finitely presented metabelian group. In addition, we prove that the same upper bound works for the relative Dehn function of a finitely generated metabelian group. We also…
In this note we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if $H$ is a finitely generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic, then $H$ has…
By an $\ell$-group $G$ we mean a lattice-ordered abelian group. This paper is concerned with the category $\FP$ of finitely presented {\it unital} $\ell$-groups, those $\ell$-groups having a distinguished order-unit $u$. Using the duality…
In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…
We describe groups elementarily equivalent to a free metabelian group with n generators. We also explore an exponentiation that naturally occurs in metabelian groups.
We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.
In this paper we classify the finite groups satisfying the following property $P_4$: their orders of representatives are set-wise relatively prime for any 4 distinct non-central conjugacy classes.
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
In this paper we study abelian and metabelian quotients of braid groups on oriented surfaces with boundary components. We provide group presentations and we prove rigidity results for these quotients arising from exact sequences related to…
In this paper we study arithmetical and structural features of a finite group that possesses exactly two conjugacy class sizes that are composite numbers.
A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…
In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…
In his paper "Finite groups have many conjugacy classes" (J. London Math. Soc (2) 46 (1992), 239-249), L. Pyber proved the to date best general lower bounds for the number of conjugacy classes of a finite group in terms of the order of the…