The spectra of almost simple groups with socle $E_7(q)$
We give an explicit description of the set of element orders for every almost simple group with socle $E_7(q)$.
math.GR↗
arXiv subjects
Alexander A. Buturlakin
Publications and source records attributed to Alexander A. Buturlakin.
The graph of atomic divisors and constructive recognition of finite simple groups
The spectrum $ω(G)$ of a finite group $G$ is the set of orders of elements of $G$. We present a polynomial-time algorithm that, given a finite set $\mathcal M$ of positive integers, outputs either an empty set or a finite simple group $G$. In the former case, there is no finite simple group $H$ with $\mathcal{M}=ω(H)$, while in the latter case, $\mathcal{M}\subseteqω(G)$ and $\mathcal{M}\neqω(H)$ for all finite simple groups $H$ with $ω(H)\neqω(G)$.
math.GR↗