Related papers: On complexity of multiplication in finite soluble …
A subgroup of a finite group is wide if each prime divisor of the group order divides the subgroup order. We obtain the description of finite soluble groups with no wide subgroups. We also prove that a finite soluble group with nilpotent…
What are simplest ways to construct a finite group from its atomic constituents? To understand part-whole relations between finite simple groups and the global structure of finite groups, we axiomatize complexity measures on finite groups.…
We study the complexity of the isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Polish spaces. For…
Given a finite group $G$, we denote by $\nu(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup. We prove that if $\nu(G)>1/12,$ then $G$ is solvable.
In this paper, we consider a problem of counting multiplicities. We fix a counting function of multiplicity of rational points in a hypersurface of a projective space over a finite field, and we give an upper bound for the sum with respect…
In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the convolution operator associated to a given…
If a soluble group $G$ contains two finitely generated abelian subgroups $A,B$ such that the number of double cosets $AgB$ is finite, then $G$ is shown to be virtually polycyclic.
We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
The mod 2 cohomology algebra of the holomorph of any finite cyclic group whose order is a power of 2 is determined.
The computational complexity of the word problem in HNN-extension of groups is studied. HNN-extension is a fundamental construction in combinatorial group theory. It is shown that the word problem for an ascending HNN-extension of a group H…
We describe finite soluble groups in which every $n$-maximal subgroup is $\mathfrak F$-subnormal.
In this paper, we investigate finite solvable tidy groups. We classify the tidy $\{ p, q \}$-groups. Combining this with a previous result, we are able to characterize the finite tidy solvable groups. Using this characterization, we bound…
We establish two-sided bounds for the complexity of two infinite series of closed orientable 3-dimensional hyperbolic manifolds, the Lobell manifolds and the Fibonacci manifolds.
We study multiplicative dependence between elements in orbits ofalgebraic dynamical systems over number fields modulo a finitely generated multiplicative subgroup of the field. We obtain a series of results, many of which may be viewed as a…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
We say that a finite almost simple $G$ with socle $S$ is admissible (with respect to the spectrum) if $G$ and $S$ have the same sets of orders of elements. Let $L$ be a finite simple linear or unitary group of dimension at least three over…
For a fixed prime $p$, we consider a filtration of the commuting complex of elements of order $p$ in the symmetric group $\mathfrak{S}_n$. The filtration is obtained by imposing successively relaxed bounds on the number of disjoint…
We develop a notion of computability and complexity of functions over the reals, which seems to be very natural when one tries to determine just how "difficult" a certain function is. This notion can be viewed as an extension of both BSS…
In this paper, we obtain an upper bound on the higher topological complexity of the total spaces of fibrations. As an application, we improve the usual dimensional upper bound on higher topological complexity of total spaces of some sphere…