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
The external morphology of Aphylidae was studied previously in detail by the two junior authors, including the description of unique derived structures formed by their lateral thoracico-abdominal region (the exponium). Here we provide an additional description of the external scent efferent system of the metathoracic scent glands of species in the genus Aphylum Bergroth, 1906 (based on scanning electron microscope study) and its connection with an autapomorphic aphylid thoracico-abdominal region, the exponium. The origins of exponial sclerites are discussed and function of the exponium is hypothesised as being part of a complex defensive mechanism in the Aphylidae., Petr Kment, Pavel Štys, Jitka Vilímová., and Obsahuje seznam literatury