A characterization of the finite simple group L16(2) by its prime graph

Khosravi, Behrooz; Khosravi, Bahman

doi:10.1007/s00229-007-0160-9

Cited by 23 publications

(11 citation statements)

References 18 publications

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“…Далее, в [14] доказано, что если и > 1 нечетны и = -простая степень, то PGL(2, ) единственным образом определяется своим графом простых чисел. В [15]- [18] получены конечные группы с таким же графом простых чисел, как у (2). А в работе [19] доказано, что некоторые ортогональные группы являются квазираспознаваемыми по графу простых чисел.…”

Section: математические заметкиunclassified

Квазираспознаваемость $^2D_{n}(3^\alpha)$ по графу простых чисел при $n=4m+1\ge 21$ и нечетном $\alpha$

Babai¹,

Хосрави²,

Khosravi³

2014

Matematicheskie Zametki

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) по графу простых чисел при n = 4m + 1 ≥ 21 и нечет-ном α, Матем. заметки, 2014, том 95, выпуск 3, 323-334 DOI: https://doi.org/10.4213/mzm10421Использование Общероссийского математического портала Math-Net.Ru под-разумевает, что вы прочитали и согласны с пользовательским соглашением

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Section: математические заметкиunclassified

Квазираспознаваемость $^2D_{n}(3^\alpha)$ по графу простых чисел при $n=4m+1\ge 21$ и нечетном $\alpha$

Babai¹,

Хосрави²,

Khosravi³

2014

Matematicheskie Zametki

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“…Then it is proved that if p and k > 1 are odd and q = p k is a prime power, then P GL (2, q) is uniquely determined by its prime graph [2] (see also [4,7]). In [12,13,16] finite groups with the same prime graph as L n (2), where n = 9, 10, 16 are obtained.…”

Section: Introductionmentioning

confidence: 99%

Quasirecognition by prime graph of finite simple groups L n (2) and U n (2)

Khosravi

Moradi

2010

Acta Math Hung

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Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, p are joined by an edge if G has an element of order pp . Let L = Ln(2) or Un (2), where n 17. We prove that L is quasirecognizable by prime graph, i.e. if G is a finite group such that Γ(G) = Γ(L), then G has a unique nonabelian composition factor isomorphic to L. As a consequence of our result we give a new proof for the recognition by element orders of Ln(2). Also we conclude that the simple group Un(2) is quasirecognizable by element orders.

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“…Also in [15] it is proved that P SL (2, p), where p > 11 is a prime number and p ≡ 1 (mod 12) is recognizable by prime graph. In [12] and [13], groups with the same prime graph as L 16 (2) and P SL (2, q) are determined.…”

Section: Introductionmentioning

confidence: 99%

Quasirecognition by prime graph of the simple group 2 F 4(q)

2009

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As the main result, we show that if G is a nite group such that Γ(G) = Γ 2 F4(q) , where q = 2 2m+1 for some m 1, then G has a unique nonabelian composition factor isomorphic to 2 F4(q). We also show that if G is a nite group satisfying |G| = 2 F4(q) and Γ(G) = Γ 2 F4(q) , then G ∼ = 2 F4(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for 2 F4(q).

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A characterization of the finite simple group L16(2) by its prime graph

Cited by 23 publications

References 18 publications

Квазираспознаваемость $^2D_{n}(3^\alpha)$ по графу простых чисел при $n=4m+1\ge 21$ и нечетном $\alpha$

Квазираспознаваемость $^2D_{n}(3^\alpha)$ по графу простых чисел при $n=4m+1\ge 21$ и нечетном $\alpha$

Quasirecognition by prime graph of finite simple groups L n (2) and U n (2)

Quasirecognition by prime graph of the simple group 2 F 4(q)

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