Recognition of simple groups U 3(Q) by element orders

Zavarnitsin, A. V.

doi:10.1007/s10469-006-0009-4

Cited by 26 publications

(24 citation statements)

References 15 publications

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“…Then, by [1], [13] and [18], oðPÞ consists of all divisors of the members of the set fr À n1; tðr À n1Þ=ð3; r À n1Þ; ðr 2 À 1Þ=ð3; r À n1Þ; ðr 2 þ nr þ 1Þ=ð3; r À n1Þg So jT n j ¼ p < ðq þ eÞ=2 ¼ jT nÀ1 j.…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%

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

Chen

Mazurov

Shi³

et al. 2007

Journal of Group Theory

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Section: Proof Of the Main Resultsmentioning

confidence: 99%

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

Chen

Mazurov

Shi³

et al. 2007

Journal of Group Theory

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“…U 4 (97) 2 13 · 3 2 · 5 · 7 6 · 67 · 97 6 · 139 · 941 (5, 5, 3, 5, 2, 3, 2, 3) (a) q ∈ {13, 17,27,31,37,43,47,53,59,61,67,73,81, 83, 97}. Let d 1 d 2 · · · d |π(G)| be the degree sequence of the prime graph GK(G).…”

Section: Od-characterization Of 4-dimensional Unitary Groupsmentioning

confidence: 99%

OD-Characterization of Some Simple Unitary Groups

Akbari

Chen

Moghaddamfar

2020

Bull. Iran. Math. Soc.

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The degree pattern of a finite group is the degree sequence of its prime graph in ascending order of vertices. We say that the problem of OD-characterization is solved for a finite group if we determine the number of pairwise nonisomorphic finite groups with the same order and degree pattern as the group under consideration. In this article the problem of OD-characterization is solved for some simple unitary groups. It was shown, in particular, that the simple unitary groups U 3 (q) and U 4 (q) are OD-characterizable, where q is a prime power < 10 2 .

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“…In Ref. [28], Zavarnitsine derived a general formula which expresses the spectrum of some automorphic extensions of a finite group of Lie type in terms of spectra of its certain subgroups.…”

Section: Spectra Of Automorphic Extensionsmentioning

confidence: 99%

Recognition by spectrum for finite simple groups of Lie type

Grechkoseeva

Shi²,

Vasil’ev

2008

Front. Math. China

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The goal of this article is to survey new results on the recognition problem. We focus our attention on the methods recently developed in this area. In each section, we formulate related open problems. In the last two sections, we review arithmetical characterization of spectra of finite simple groups and conclude with a list of groups for which the recognition problem was solved within the last three years.

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Recognition of simple groups U 3(Q) by element orders

Cited by 26 publications

References 15 publications

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

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

OD-Characterization of Some Simple Unitary Groups

Recognition by spectrum for finite simple groups of Lie type

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