Complex linear groups of degree at most v − 3

Ferguson, Pamela A.

doi:10.1016/0021-8693(85)90158-9

Cited by 7 publications

(4 citation statements)

References 18 publications

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supporting

confidence: 87%

“…By the classification of finite simple groups, G is isomorphic to a sporadic simple group. It is easy to check by the Atlas [14] This result is similar to that of Ferguson [10].…”

Section: Set G = G/z(g)supporting

confidence: 55%

“…In the present paper, under the assumption that 7 is Abelian, we will characterize the linear groups of degree less than p -2 in terms of group theoretical properties. Our results extend the main theorem of Ferguson [10].All groups in this paper are assumed to be finite, and the notation and terminology are standard and follow that of [7] and [14].Linear groups of degree at most 4 have been determined [2], [ 15]. Therefore we will assume in the following that p is greater than 5.…”

mentioning

confidence: 61%

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On linear groups over finite fields

Zhang¹

1990

Proc. Amer. Math. Soc.

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In 1963, R. Brauer raised forty-three important problems on group and representation theories [2]. The fortieth problem is as follows:Brauer Problem 40. Determine the linear groups G of small degrees over a finite field 7. 7 is cyclic. Since SL(2, p") has all d with 2 < d < p -1 as the dimension of an irreducible representation over a suitably large finite field of characteristic p, it is in general rather difficult to determine the group structure of a linear group over a finite field. In the present paper, under the assumption that 7 is Abelian, we will characterize the linear groups of degree less than p -2 in terms of group theoretical properties. Our results extend the main theorem of Ferguson [10].All groups in this paper are assumed to be finite, and the notation and terminology are standard and follow that of [7] and [14].Linear groups of degree at most 4 have been determined [2], [ 15]. Therefore we will assume in the following that p is greater than 5.

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supporting

confidence: 87%

“…By the classification of finite simple groups, G is isomorphic to a sporadic simple group. It is easy to check by the Atlas [14] This result is similar to that of Ferguson [10].…”

Section: Set G = G/z(g)supporting

confidence: 55%

mentioning

confidence: 61%

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On linear groups over finite fields

Zhang¹

1990

Proc. Amer. Math. Soc.

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“…In particular, complex irreducible finite linear groups of degree at most p -1, where p is a prime divisor of the gToup order, were described in [102]. This result extended an earlier result of [16], where groups of degree at most p -3 were classified.…”

Section: Groups Of Relatively Small Degree: Zero Characteristicsupporting

confidence: 72%

Some aspects of finite linear groups: A survey

Tiep¹,

Zalesskiǐ²

2000

J Math Sci

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Finite linear groups have been studied since the beginning of the century. The goal of this survey is to reflect recent results in this area, obtained mostly in the 90's and using the classification of fnite simple groups. It is a pleasure to thank the Institute for its hospitality. Linear Groups of Small DegreeLinear groups of degree <4 were classified at the beginning of the century, both for the zero and the prime characteristic cases, by using a kind of geometrical approach. New ideas, based on the representation theory elaborated by Brauer, Feit, and their successors, made it possible to classify linear groups of degree up

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Complex linear groups of relatively small degree

Ferguson

1983

Journal of Algebra

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Complex linear groups of degree at most v − 3

Cited by 7 publications

References 18 publications

On linear groups over finite fields

On linear groups over finite fields

Some aspects of finite linear groups: A survey

Complex linear groups of relatively small degree

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