An n × n ray pattern A is called a spectrally arbitrary ray pattern if the complex matrices in Q(A) give rise to all possible complex polynomials of degree n. In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an n×n irreducible spectrally arbitrary ray pattern is 3n-1. In this paper, we introduce a new family of spectrally arbitrary ray patterns of order n with exactly 3n - 1 nonzeros., Yinzhen Mei, Yubin Gao, Yanling Shao, Peng Wang., and Obsahuje seznam literatury
For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. In 1980s, J. G. Thompson posed the following conjecture: If $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N(G) = N(L)$, then $G\cong L$. We prove this conjecture for an infinite class of simple groups. Let $p$ be an odd prime. We show that every finite group $G$ with the property $Z(G)=1$ and $N(G) = N(A_i)$ is necessarily isomorphic to $A_i$, where $i\in\{2p,2p+1\}$., Azam Babai, Ali Mahmoudifar., and Obsahuje bibliografii