Trinomials with non-conjugate roots of the same prime order
نویسندگان
چکیده
منابع مشابه
Roots of Trinomials over Prime Fields
The origin of this work was the search for a “Descartes’ rule” for finite fields a nontrivial upper bound for the number of roots of sparse polynomials. In [2], Bi, Cheng, and Rojas establish such an upper bound. Then, in [3], Cheng, Gao, Rojas, and Wan show that the bound is essentially optimal in an infinite number of cases by constructing t-nomials with many roots in Fpt . However, the bound...
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Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...
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(a) f has two distinct roots with identical norm v if and only if p is located on a real double point of the hypotrochoid, (b) f has a root of multiplicity 2 with norm v if and only if the corresponding hypotrochoid is a hypocycloid and p is a cusp of it, and (c) f has more than two roots with norm v if and only if p = 0 if and only if the hypotrochoid is a rhodonea curve with a multiple point ...
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The prime graph of a finite group $G$ is denoted by$ga(G)$. A nonabelian simple group $G$ is called quasirecognizable by primegraph, if for every finite group $H$, where $ga(H)=ga(G)$, thereexists a nonabelian composition factor of $H$ which is isomorphic to$G$. Until now, it is proved that some finite linear simple groups arequasirecognizable by prime graph, for instance, the linear groups $L_...
متن کاملFinite groups with $X$-quasipermutable subgroups of prime power order
Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1971
ISSN: 0097-3165
DOI: 10.1016/0097-3165(71)90059-8