Related papers: On the behavior of $\pi$-submaximal subgroups unde…
We determine the structure of the finite groups with the property that every cyclic subgroup is the intersection of maximal subgroups, comparing this property with the one where all proper subgroups are intersections of maximal subgroups.
A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…
For a finite group $G$ we investigate the difference between the maximum size MaxDim$(G)$ of an "independent" family of maximal subgroups of $G$ and maximum size $m(G)$ of an irredundant sequence of generators of $G$. We prove that…
A homogeneous family of subsets over a given set is one with a very ``rich'' automorphism group. We prove the existence of a bi-universal element in the class of homogeneous families over a given infinite set and give an explicit…
We look at group actions on metric spaces, particularly at group actions on geodesic hyperbolic spaces. We classify the types of automorphisms on these spaces and prove several results about the density of the hyperbolic limit set of the…
For a finite group $G$, let $\sigma(G)$ be the number of subgroups of $G$ and $\sigma_\iota(G)$ the number of isomorphism types of subgroups of $G$. Let $L=L_r(p^e)$ denote a simple group of Lie type, rank $r$, over a field of order $p^e$…
In this talk, we'll present some recent results related to group actions in several complex variables. We'll not aim at giving a complete survey about the topic but giving some our own results and related ones. We'll divide the results into…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
In this communication, the co-maximal subgroup graph $\Gamma(G)$ of a finite group $G$ is examined when $G$ is a finite nilpotent group, finite abelian group, dihedral group $D_n$, dicyclic group $Q_{2^n}$, and $p$-group. We derive the…
In this note we study topological invariants of the spaces of homomorphisms Hom(\pi,G), where \pi\ is a finitely generated abelian group and G is a compact Lie group arising as an arbitrary finite product of the classical groups SU(r), U(q)…
In the paper we consider the following conjecture: if a finite group $G$ possesses a solvable $\pi$-Hall subgroup $H$, then there exist elements $x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\cap H^t=O_\pi(G)$ holds. The…
In this paper, we give an introduction for rough groups and rough homomorphisms. Then we present some properties related to topological rough subgroups and rough subsets. We construct the product of topological rough groups and give an…
We consider the structure of finite $p$-groups $G$ having precisely three characteristic subgroups, namely $1$, $\Phi(G)$ and $G$. The structure of $G$ varies markedly depending on whether $G$ has exponent $p$ or $p^2$, and, in both cases,…
Heterogeneity is one important feature of complex systems, leading to the complexity of their construction and analysis. Moving the heterogeneity at model level helps in mastering the difficulty of composing heterogeneous models which…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
We introduce the concept of hyperreflection groups, which are a generalization of Coxeter groups. We prove the Deletion and Exchange Conditions for hyperreflection groups, and we discuss special subgroups and fundamental sectors of…
A function field over a finite field is called maximal if it achieves the Hasse-Weil bound. Finding possible genera that maximal function fields achieve has both theoretical interest and practical applications to coding theory and other…
We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.
Recall that a $p$-group of order $p^ {n} >p^ {3} $ is of maximal class, if its nilpotency class is $n-1$. In this paper, we study the $p$-groups of maximal class. Furthermore, we introduce a subgroup of a $p$-group of maximal class called…