Order of elements in the groups related to the general linear group

Darafsheh, M. R.

doi:10.1016/j.ffa.2004.12.003

Cited by 28 publications

(14 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now H ∩ PGL(V ) 2 2m .Sp 2m (2), where 2 2m is elementary abelian of order 2 2m , so |z| ≤ 2α for all z ∈ H ∩ PGL(V ) where α is the maximal order of an element of Sp 2m (2). Clearly α ≤ 2 2m − 1 (see [17,Corollary 2], for example), so by considering (29) we reduce to the case (n, q) = (8,5). Here α = 15 and |y| ≥ (5 3 + 1)/4, so there are no C 6 -subgroups in M. In this way we deduce that (30) holds and the result quickly follows.…”

Section: Graph Automorphismsmentioning

confidence: 86%

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On the uniform spread of almost simple linear groups

Burness¹,

Guest²

2013

Nagoya Mathematical Journal

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Abstract. Let G be a finite group and let k be a non-negative integer. We say that G has uniform spread k if there exists a fixed conjugacy class C in G with the property that for any k nontrivial elements x1, . . . , x k in G there exists y ∈ C such that G = xi, y for all i. Further, the exact uniform spread of G, denoted by u(G), is the largest k such that G has the uniform spread k property. By a theorem of Breuer, Guralnick and Kantor, u(G) ≥ 2 for every finite simple group G. Here we consider the uniform spread of almost simple linear groups. Our main theorem states that if G = PSLn(q), g is almost simple then u(G) ≥ 2 (unless G ∼ = S6), and we determine precisely when u(G) tends to infinity as |G| tends to infinity.

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Section: Graph Automorphismsmentioning

confidence: 86%

“…The excluded case G = PSL 3 (4).2 1 is a genuine exception to the bound in (17), but it is easy to check that u(G) ≥ 2 (see Proposition 2.18).…”

Section: Graph-field Automorphismsmentioning

confidence: 99%

On the uniform spread of almost simple linear groups

Burness¹,

Guest²

2013

Nagoya Mathematical Journal

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“…Indeed, L k r is a 2-transitive permutation group of degree p, see [17,Lemma 8.29]. Notice that SL k r has elements of order p see [9,Corollary 3]. On the other hand, a Sylow p-subgroup of L k r has order p, it is self-centralizer and its normalizer has order pk.…”

Section: On Projective Special Linear Groupsmentioning

confidence: 99%

Conjugacy Classes ofP-Cycles of Type D in Alternating Groups

Fantino

2014

Communications in Algebra

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“…We know that the order of any element in L 2 (q) is either p or it is a divisor of q+1 2 or q−1 2 . By [6] the maximum order of an element of L 2 (q) is Let ρ be an independent set in GK(G) containing 1093. By the remark made after Lemma 1, at least two of the primes in ρ divide |S|.…”

Section: Proof Of the Main Theoremmentioning

confidence: 99%