Related papers: Finite groups with integer harmonic mean of elemen…
Under reasonable assumptions, a group action on a module extends to the minimal free resolutions of the module. Explicit descriptions of these actions can lead to a better understanding of free resolutions by providing, for example,…
All beta-type functions, which are p-homogeneous, are determined. Applying this result, we show that a beta-type function is a homogeneous mean iff it is the harmonic one. A reformulation of a result due to Heuvers in terms of a Cauchy…
To avoid problems with infinite measure, the functional integral for harmonic oscillator can be calculated by time - slicing method with continuum limit procedure proposed Gelfand and Yaglom. In previous article we proved by nonperturbative…
The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. The main object of this paper is to obtain a characterization for all finite groups of odd order with commutativity degree…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
We give a simple algorithm that enables us to determine whether a subgroup of finite index of the Hecke group is normal.
This paper proposes a quantum circuit for computing the mean value from a given set of numbers or function evaluations. Suppose a Quantum Random Access Memory is given as a black-box function, which allows us to store and read the values of…
An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.
This paper investigates certain classes of entire functions in C^n that, together with their partial derivatives, share a finite set consisting of three elements. By employing normality criteria, we study the behaviour of such functions and…
Let $G$ be a finite group and let $\psi(G)$ denote the sum of element orders of $G$. It is well-known that the maximum value of $\varphi$ on the set of groups of order $n$, where $n$ is a positive integer, will occur at the cyclic group…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.
The object of this paper is to examine finite solvable groups whose integral group rings have only trivial central units.
In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…
The purpose of the present article is to obtain the condition that the function defined by infinite composition of entire functions becomes an entire function. Moreover, as an example of such functions, we study a function called Poincare…
We define and study the interpolated finite multiple harmonic $q$-series. A generating function of the sums of the interpolated finite multiple harmonic $q$-series with fixed weight, depth and $i$-height is computed. Some Ohno-Zagier type…
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
Let M=M(n,q) be the average of the orders of the elements in the finite unitary group U(n,q). The asymptotic estimate log(M)=nlog(q)-log(n) +o(log n) is proved.
We provide approximations to the prime counting function by various discretized versions of the logarithmic integral function, expressed solely in terms of the harmonic numbers. We demonstrate with explicit error bounds that these…
Given a non-negative integer $n$, we establish a formula for the number of finite magmas on a set with cardinality $n$ up to isomorphism. We then generalize the method to operations with arbitrary finite arity, which yields a corrected…