On the Frattini lemma

Let $K$ be a subgroup of a finite group $G$, and suppose that $G=KN_G(P)$ for every Sylow subgroup $P$ of $K$. Then the subgroup $K$ is normal in $G$

The Nilpotency Criterion for the Derived Subgroup of a Finite Group

It is proved that the derived subgroup of a finite group is nilpotent if and only if $|ab|\ge |a||b|$ for all primary commutators $a$ and $b$ of coprime orders

Analysis Of Congestion Control In Data Channels With Frequent Frame Loss

Development of optimal control procedures for congested networks is a key factor in maintaining efficient network utilization. The absence of congestion control mechanism or its failure can lead to the lack of availability for certain network segments, and in severe cases -- for the entire network. The paper presents an analytical model describing the operation of the TCP Reno congestion control algorithm in terms of differential calculus and queuing systems. The purpose of this research is to explore the possibilities and ways of increasing the virtual channel capacity utilization efficiency in a lossy environment.Comment: 5 pages, 4 figures, 2nd European Conference on Electrical Engineering & Computer Science EECS 2018: Bern, Switzerland, December 20-22, 201

Simulation Model Of Functional Stability Of Business Processes

Functioning of business processes of high-tech enterprise is in a constant interaction with the environment. Herewith a wide range of such interaction represents a variety of conflicts affecting the achievement of the goals of business processes. All these things lead to the disruption of functioning of business processes. That's why modern enterprises should have mechanisms to provide a new property of business processes - ability to maintain and/or restore functions in various adverse effects. This property is called functional stability of business processes (FSBP). In this article we offer, showcase and test the new approach to assessing the results of business process re-engineering by simulating their functional stability before and after re-engineering.Comment: 10 pages, 12 figure

On a finite group having a normal series whose factors have bicyclic Sylow subgroups

We consider the structure of a finite groups having a normal series whose factors have bicyclic Sylow subgroups. In particular, we investigated groups of odd order and $A_4$-free groups with this property. Exact estimations of the derived length and nilpotent length of such groups are obtained.Comment: 9 page

On factorized groups with permutable subgroups of factors

The subgroups $A$ and $B$ of a group~$G$ are called {\rm msp}-permutable, if the following statements hold: $AB$~is a subgroup of~$G$; the subgroups $P$ and $Q$ are mutually permutable, where $P$~is an arbitrary Sylow $p$-subgroup of~$A$ and $Q$~is an arbitrary Sylow $q$-subgroup of~$B$, ${p\neq q}$. In the present paper, we investigate groups that factorized by two {\rm msp}-permutable subgroups. In particular, the supersolubility of the product of two supersoluble {\rm msp}-permutable subgroups is proved

Finite Groups with Hall Schmidt Subgroups

A Schmidt group is a non-nilpotent group whose every proper subgroup is nilpotent. We study the properties of a non-nilpotent group G in which every Schmidt subgroup is a Hall subgroup of G.Comment: 9 page

A note on the supersolvability of a finite group with prime index of some subgroups

In this paper, we proved that a group $G$ is supersoluble if and only if for any prime $p\in \pi (G)$ there exists a supersoluble subgroup of index $p$

Finite soluble groups with nilpotent wide subgroups

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 wide subgroups has the quotient group by its hypercenter with no wide subgroups

On Maximal Subgroups of a Finite Solvable Group

The following result is received: Let $H$ be a non-normal maximal subgroup of a finite solvable group $G$ and let $q \in \pi(F(H/\mathrm{Core}_GH))$, then $G$ has a Sylow $q$-subgroup $Q$ such that $N_{G}(Q) \subseteq H$