quasirecognition by prime graph of $u_3(q)$ where $2 < q =p^{alpha} < 100$

نویسندگان

seyed sadegh salehi amiri

islamic azad university alireza khalili asboei

islamic azad university ali iranmanesh

tarbiat modares university abolfazl tehranian

islamic azad university

چکیده

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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عنوان ژورنال:
international journal of group theory

جلد ۱، شماره ۳، صفحات ۵۱-۶۶

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