quasirecognition by prime graph of $u_3(q)$ where $2 < q =p^{alpha} < 100$
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abstract
let $g $ be a finite group and let $gamma(g)$ be the prime graph of g. assume $2 < q = p^{alpha} < 100$. we determine finite groups g such that $gamma(g) = gamma(u_3(q))$ and prove that if $q neq 3, 5, 9, 17$, then $u_3(q)$ is quasirecognizable by prime graph, i.e. if $g$ is a finite group with the same prime graph as the finite simple group $u_3(q)$, then $g$ has a unique non-abelian composition factor isomorphic to $u_3(q)$. as a consequence of our results, we prove that the simple groups $u_{3}(8)$ and $u_{3}(11)$ are $4-$recognizable and $2-$recognizable by prime graph, respectively. in fact, the group $u_{3}(8)$ is the first example which is a $4-$recognizable by prime graph.
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Journal title:
international journal of group theoryجلد ۱، شماره ۳، صفحات ۵۱-۶۶
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