Related papers: On complexity of multiplication in finite soluble …

(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…

Given a group $G$ we write $h(G)$ to denote the maximum number of times that a field extension of $\mathbb{Q}$ appears as the field of values of a conjugacy class of a group. In this work, we prove that $|G|$ is bounded in terms of $h(G)$.…

For a finite group $G$, we study the probability $sp(G)$ that, given two elements $x,y \in G$, the cyclic subgroup $\langle x \rangle$ is subnormal in the subgroup $\langle x, y \rangle$. This can be seen as an intermediate invariant…

While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the…

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…

In this paper we obtain significant bounds for the number of maximal subgroups of a given index of a finite group. These results allow us to give new bounds for the number of random generators needed to generate a finite $d$-generated group…

We provide a new upper bound on the number of conjugacy classes in the group $U_n(q)$ of unitriangular matrices over a finite field. We also compute a similar upper bound for every group in the lower central series of $U_n(q)$.

We solve two open problems concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a left ideal or a suffix-closed language with $n$ left quotients (that is, with state complexity $n$) is at most…

Lower bounds for some explicit decision problems over the complex numbers are given.

In this paper, we provide some conditions of (super)-solvability and nilpotency of a finite group $G$ based on its number of subgroups $Sub(G)$. Our results generalize the classification of finite groups with less than $20$ subgroups by…

We compare the volume of a hyperbolic 3-manifold $M$ of finite volume and the complexity of its fundamental group.

This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…

We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.

In this paper we are concerned with finite soluble groups $G$ admitting a factorisation $G=AB$, with $A$ and $B$ proper subgroups having coprime order. We are interested in bounding the Fitting height of $G$ in terms of some…

We give upper bounds of the Matveev complexities of two-bridge link complements by constructing their spines explicitly. In particular, we determine the complexities for an infinite sequence of two-bridge links corresponding to the…

We describe quantizations on monoidal categories of modules over finite groups. They are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over S3 and A4 we are given…

We establish upper bounds of bit complexity of computing solution operators for symmetric hyperbolic systems of PDEs. Here we continue the research started in in our revious publications where computability, in the rigorous sense of…

We show that only a rather small proportion of linear equations are solvable in elements of a fixed finitely generated subgroup of a multiplicative group of a number field. The argument is based on modular techniques combined with a…

The incompressibility method is a counting argument in the framework of algorithmic complexity that permits discovering properties that are satisfied by most objects of a class. This paper gives a preliminary insight into Kolmogorov's…

We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.