Uniform <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-generation of the 4-dimensional classical groups

Pellegrini, Marco Antonio; Bellani, M.C. Tamburini; Vsemirnov, Maxim

doi:10.1016/j.jalgebra.2012.06.027

Journal of Algebra

2012

DOI: 10.1016/j.jalgebra.2012.06.027

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Uniform (2,k)-generation of the 4-dimensional classical groups

Marco Antonio Pellegrini

M.C. Tamburini Bellani

Maxim Vsemirnov

Abstract: In this paper we study the (2, k)-generation of the finite classical groups SL 4 (q), Sp 4 (q), SU 4 (q 2 ) and their projective images. Here k is the order of an arbitrary element of SL 2 (q), subject to the necessary condition k 3. When q is even we allow also k = 4.

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Cited by 13 publications

References 24 publications

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Generation of finite simple groups by an involution and an element of prime order

King

2017

Journal of Algebra

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We prove that every non-abelian finite simple group is generated by an involution and an element of prime order. Preliminary resultsThe p2, 3q-generation of classical groups has been studied extensively, and there are many results for groups of small dimension that we will make use of.Lemma 2.1. If G is a finite simple classical group listed in Table 2, then G is p2, 3qgenerated.We note that though there are many other p2, 3q-generation results regarding classical groups, our method will not require them.Lemma 2.2. If G is listed in Table 3 then G is p2, pq-generated, where p P t5, 7u is specified.Proof. Let G " P SL 3 p4q and p " 7. By [7] the only maximal subgroups M of G with order divisible by 7 are isomorphic to P SL 2 p7q. The index of M " P SL 2 p7q in G is 120

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Generation of finite simple groups by an involution and an element of prime order

King

2017

Journal of Algebra

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The (2,3)-generation of the finite unitary groups

Pellegrini

Bellani

2020

Journal of Algebra

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On the (2,3)-generation of the finite symplectic groups

Pellegrini

Bellani

2022

Journal of Algebra

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Uniform (2,k)-generation of the 4-dimensional classical groups

Abstract: In this paper we study the (2, k)-generation of the finite classical groups SL 4 (q), Sp 4 (q), SU 4 (q 2 ) and their projective images. Here k is the order of an arbitrary element of SL 2 (q), subject to the necessary condition k 3. When q is even we allow also k = 4.

Cited by 13 publications

References 24 publications

Generation of finite simple groups by an involution and an element of prime order

Generation of finite simple groups by an involution and an element of prime order

The (2,3)-generation of the finite unitary groups

On the (2,3)-generation of the finite symplectic groups

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