A Recognition Algorithm For Classical Groups Over Finite Fields

Niemeyer, Alice C.; Praeger, Cheryl E.

doi:10.1112/s0024611598000422

Cited by 59 publications

(87 citation statements)

References 20 publications

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Order By: Relevance

“…This leaves case (b) of [NP1,Theorem 4.7], and in that case G is conjugate to a subgroup of GL( (1) holds. In the latter case, since each of r, s is at least f + 1 > c, it follows that x c , y…”

Section: Primitive Prime Divisorsmentioning

confidence: 99%

A new solvability criterion for finite groups

Dolfi

Guralnick

Herzog

et al. 2011

Journal of the London Mathematical Society

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Abstract. In 1968, John Thompson proved that a finite group G is solvable if and only if every 2-generator subgroup of G is solvable. In this paper, we prove that solvability of a finite group G is guaranteed by a seemingly weaker condition: G is solvable if for all conjugacy classes C and D of G, there exist x ∈ C and y ∈ D for which x, y is solvable. We also prove the following property of finite nonabelian simple groups, which is the key tool for our proof of the solvability criterion: if G is a finite nonabelian simple group, then there exist two integers a and b which represent orders of elements in G and for all elements x, y ∈ G with |x| = a and |y| = b, the subgroup x, y is nonsolvable.

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Section: Primitive Prime Divisorsmentioning

confidence: 99%

A new solvability criterion for finite groups

Dolfi

Guralnick

Herzog

et al. 2011

Journal of the London Mathematical Society

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show abstract

“…Niemeyer & Praeger [88] answer the equivalent question for an arbitrary classical group. This they do by refining a classification by Guralnick et al [51] [94].…”

Section: Classical Groups In Natural Representationmentioning

confidence: 99%

Algorithms for matrix groups

O’Brien

2011

Groups St Andrews 2009 in Bath

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“…This theorem was followed by others [NiP,CLG1] that decide, similarly, whether or not a given subgroup G = X ≤ GL(d, q) contains a classical group defined on V as a normal subgroup.…”

Section: Nonconstructive Recognition Of Simple Groupsmentioning

confidence: 99%

“…Nevertheless, it is possible to determine qualitative properties of |g| without actually computing the order. There are algorithms in [NeP1,NiP,KS2] that can be used to decide whether or not |g| is divisible by some primitive prime divisor 3 of p k − 1 for a given prime p and given exponent k.…”

Section: Matrix Groupsmentioning

confidence: 99%

Computing with matrix groups

Kantor¹

2003

Groups, Combinatorics and Geometry

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A Recognition Algorithm For Classical Groups Over Finite Fields

Cited by 59 publications

References 20 publications

A new solvability criterion for finite groups

A new solvability criterion for finite groups

Algorithms for matrix groups

Computing with matrix groups

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