Recognition of the simple groups L3(q) by element orders

Zavarnitsine, Andrei V.

doi:10.1515/jgth.2003.044

Cited by 32 publications

(31 citation statements)

References 19 publications

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“…By (12) and (10), we have j − s > 8 > 2, 3; n − j − r > 8 > 2, 3; and n − s − r = (n − j − r) + (j − s) > 8 + 8 = 16. Thus (n − s − r, j − s) is an admissible pair and by induction we have n − s − r = n 1 + · · · + n k and j − s = n 1 + · · · + n k .…”

Section: [εN]mentioning

confidence: 92%

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Properties of element orders in covers for Ln(q) and Un(q)

Zavarnitsine

2008

Sib Math J

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We show that if a finite simple group G, isomorphic to PSL n (q) or PSU n (q) where either n = 4 or q is prime or even, acts on a vector space over a field of the defining characteristic of G; then the corresponding semidirect product contains an element whose order is distinct from every element order of G. We infer that the group PSL n (q), n = 4 or q prime or even, is recognizable by spectrum from its covers thus giving a partial positive answer to Problem 14.60 from the Kourovka Notebook.

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Section: [εN]mentioning

confidence: 92%

“…Let G be a proper cover for H of minimal order such that ω(H) = ω(G). By [12,Lemma 12], we may assume that G = N H, where H acts on the elementary abelian r-group N irreducibly. Suppose that this action is not absolutely irreducible.…”

Section: Lemmamentioning

confidence: 99%