Recognition of the finite almost simple groups PGL2(q) by their spectrum

Chen, G. Y; Mazurov, V. D.; Shi, Wujie; Vasil’ev, A. V.; Zhurtov, A. Kh.

doi:10.1515/jgt.2007.007

Cited by 11 publications

(9 citation statements)

References 16 publications

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“…This means that every simple group can be characterized by pure quantitative properties. It is also proved by Chen, Mazurov and Shi et al in [7] that if q is not a prime, and also q = 9, and G is a group with π e (G) = π e (P GL(2, q)), then G ≃ P GL(2, q). In the exceptional cases, there are infinitely many pairwise non-isomorphic groups G such that π e (G) = π e (P GL(2, q)).…”

Section: Denote By T (G) = {π I (G) | 1 I T(g)} the Set Of All Connecmentioning

confidence: 84%

A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

Li¹,

Shi²,

Yu³

2015

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we characterize some P GL(2, q) by their orders and maximum element orders. We also prove that P SL(2, p) with p 3 a prime can be determined by their orders and maximum element orders. Moreover, we show that, in general, if q = p n with p a prime and n > 1, P GL(2, q) can not be uniquely determined by their orders and maximum element orders. Several known results are generalized.

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Section: Denote By T (G) = {π I (G) | 1 I T(g)} the Set Of All Connecmentioning

confidence: 84%

A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

Li¹,

Shi²,

Yu³

2015

Bulletin of the Korean Mathematical Society

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“…But H ¢ G, which implies that H ⊆ Z(G) and we get a contradiction. So G/H ∼ = PGL(2, 5), which implies that H = 1 and G ∼ = PGL (2,5).…”

Section: By Lemma 29 We Havementioning

confidence: 94%

Some New Characterizations for PGL(2, q)

Khosravi

Khatami

Akhlaghi

2011

Cubo

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Many authors introduced some characterizations for finite groups. In this paper as the main result we prove that the finite group PGL(2, q) is uniquely determined by its noncommuting graph. Also we prove that PGL(2, q) is characterizable by its noncyclic graph. Throughout the proof of these results we prove that PGL(2, q) is uniquely determined by its order components and using this fact we give positive answer to a conjecture of Thompson and another conjecture of Shi and Bi for the group PGL(2, q). RESUMENMuchos autores introdujeron algunas caracterizaciones de los grupos finitos. En este trabajo como principal resultado se demuestra que grupo finito PGL(2, q) es determinado nicamente por su gráfica no conmutativa. También se demuestra que PGL(2, q) 13, 2 (2011) es caracterizable por su gráfico no cíclico. A lo largo de la prueba de estos resultados se demuestra que PGL(2, Q) es determinadoúnicamente por los componentes de su orden y con ello damos respuesta positiva a una conjetura de Thompson y otra conjetura de Shi Bi y para el grupo PGL(2, q).

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“…Also characterization by prime graph is in general harder to establish than recognizability by element orders since some methods fail in the former case. Therefore as a consequence of our Main Theorem, we give a new proof for the main result in [4], where p is a prime and k > 1 is an odd integer. Throughout the proof we use the classification of finite simple groups and we use Tables 1-3.…”

Section: Introductionmentioning

confidence: 94%

“…In [4], it is proved that if q = p α , where p is a prime and α > 1, then PGL(2, q) is uniquely determined by its element orders. In this paper as the main result we prove the following theorem:…”

Section: Introductionmentioning

confidence: 99%

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CHARACTERIZATION BY PRIME GRAPH OF PGL(2, p^k) WHERE p AND k > 1 ARE ODD

Akhlaghi

Khosravi

Khatami

2010

Int. J. Algebra Comput.

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Int. J. Algebra Comput. 2010.20:847-873. Downloaded from www.worldscientific.com by UNIVERSITY OF SEVILLE on 02/05/15. For personal use only. Characterization by Prime Graph of PGL(2, p k ) 849 divisor of positive integers a and b, and by [a, b] the least common multiple of positive integers a and b. Let m be a positive integer and p be a prime number.Then |m| p denotes the p-part of m. In other words, |m| p = p k if p k | m but p k+1 m. Preliminary ResultsRemark 2.

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Recognition of the finite almost simple groups PGL2(q) by their spectrum

Cited by 11 publications

References 16 publications

A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

Some New Characterizations for PGL(2, q)

CHARACTERIZATION BY PRIME GRAPH OF PGL(2, p^k) WHERE p AND k > 1 ARE ODD

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Recognition of the finite almost simple groups PGL2(q) by their spectrum

Cited by 11 publications

References 16 publications

A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

Some New Characterizations for PGL(2, q)

CHARACTERIZATION BY PRIME GRAPH OF PGL(2, pk) WHERE p AND k > 1 ARE ODD

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CHARACTERIZATION BY PRIME GRAPH OF PGL(2, p^k) WHERE p AND k > 1 ARE ODD