On the partial Π \Pi -property of some subgroups of prime power order of finite groups

Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies the partial $\Pi$-property in $G$ if if there exists a chief series $\varGamma_{G}: 1 =G_{0} < G_{1} < \cdot\cdot\cdot < G_{n}= G$ of $G$ such that for every $G$-chief factor $G_{i}/G_{i-1} (1\leq i\leq n)$ of $\varGamma_{G}$, $| G / G_{i-1} : N_{G/G_{i-1}} (HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1})|$ is a $\pi (HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1})$-number. In this paper, we study the influence of some subgroups of prime power order satisfying the partial $\Pi$-property on the structure of a finite group.Comment: arXiv admin note: substantial text overlap with arXiv:2304.11451. text overlap with arXiv:1301.6361 by other author

On Π\Pi -property of some maximal subgroups of Sylow subgroups of finite groups

summary:Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies the $\Pi$-property in $G$ if for any chief factor $L / K$ of $G$, $| G / K : N_{G / K} ( HK/K\cap L/K )|$ is a $\pi (HK/K\cap L/K)$-number. We study the influence of some $p$-subgroups of $G$ satisfying the $\Pi$-property on the structure of $G$, and generalize some known results

Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism

This paper is focused on the stabilization of Takagi–Sugeno fuzzy model-based Markovian jump systems with the aid of a delayed state observer. Due to network-induced constraints in the communication channel, a delay partition method combined with an event-triggered mechanism is proposed to design the observer. Then, a novel integral sliding surface is designed, based on which sliding mode dynamics is obtained. Further, according to stochastic stability theory, feasible conditions are provided to ensure the sliding mode dynamics and the error dynamics have an H∞ attenuate level γ. The challenge is to deal with the issue that transition rates may be totally unknown. Moreover, an observer-based sliding mode controller is constructed to ensure the finite-time reachability of the predefined sliding surface. Finally, a numerical example based on a robotic manipulator is given to verify the effectiveness of the proposed method

Robot Static Path Planning Method Based on Deterministic Annealing

Heuristic calculation is an essential method to solve optimisation problems. However, its vast computing requirements limit its real-time and online applications, especially in embedded systems with limited computing resources, such as mobile robots. This paper presents a robot path planning algorithm called DA-APF based on deterministic annealing. It is derived from the artificial potential field and can effectively solve the local minimum problem of the model established by the potential field method. The calculation performance of DA-APF is considerably improved by introducing temperature parameters to enhance the potential field function and by using annealing and tempering methods. Moreover, an optimal or near-optimal robot path planning scheme is given. A comprehensive case study is performed using heuristic methods, such as genetic algorithm and simulated annealing. Simulation results show that DA-APF performs well in various static path planning environments