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Central European Journal of Mathematics

, Volume 6, Issue 3, pp 384–392 | Cite as

Periodic subgroups of projective linear groups in positive characteristic

  • Alla S. Detinko
  • Dane L. Flannery
Research Article
  • 28 Downloads

Abstract

We classify the maximal irreducible periodic subgroups of PGL(q, \( \mathbb{F} \) ), where \( \mathbb{F} \) is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and \( \mathbb{F} \) × has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, \( \mathbb{F} \) ) containing the centre \( \mathbb{F} \) ×1 q of GL(q, \( \mathbb{F} \) ), such that G/\( \mathbb{F} \) ×1 q is a maximal periodic subgroup of PGL(q, \( \mathbb{F} \) ), and if H is another group of this kind then H is GL(q, \( \mathbb{F} \) )-conjugate to a group in the list. We give criteria for determining when two listed groups are conjugate, and show that a maximal irreducible periodic subgroup of PGL(q, \( \mathbb{F} \) ) is self-normalising.

Keywords

linear group periodic group projective general linear group field classification 

MSC

20H20 20Exx 

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Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alla S. Detinko
    • 1
  • Dane L. Flannery
    • 1
  1. 1.Department of MathematicsNational University of IrelandGalwayIreland

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