Periodic subgroups of projective linear groups in positive characteristic

Alla S. Detinko, Dane L. Flannery

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We classify the maximal irreducible periodic subgroups of PGL(q, F), where F is a field of positive characteristic p transcendental over its prime subfield, q ≠ p is prime, and F× has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, F) containing the centre F× 1q of GL(q, F), such that G/F×1q is a maximal periodic subgroup of PGL(q, F), and if H is another group of this kind then H is GL(q, 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, F) is self-normalising.

Original languageEnglish
Pages (from-to)384-392
Number of pages9
JournalCentral European Journal of Mathematics
Issue number3
Early online date18 Jun 2008
Publication statusPublished - 1 Sep 2008
Externally publishedYes


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