We classify the maximal irreducible periodic subgroups of PGL(q, ), where is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and × has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, ) containing the centre ×1q of GL(q, ), such that G/ ×1q is a maximal periodic subgroup of PGL(q, ), and if H is another group of this kind then H is GL(q, )-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, ) is self-normalising.
@article{bwmeta1.element.doi-10_2478_s11533-008-0033-9,
author = {Alla Detinko and Dane Flannery},
title = {Periodic subgroups of projective linear groups in positive characteristic},
journal = {Open Mathematics},
volume = {6},
year = {2008},
pages = {384-392},
zbl = {1159.20026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0033-9}
}
Alla Detinko; Dane Flannery. Periodic subgroups of projective linear groups in positive characteristic. Open Mathematics, Tome 6 (2008) pp. 384-392. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0033-9/
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