Periodic subgroups of projective linear groups in positive characteristic
Open Mathematics (2008)
- Volume: 6, Issue: 3, page 384-392
- ISSN: 2391-5455
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topAlla Detinko, and Dane Flannery. "Periodic subgroups of projective linear groups in positive characteristic." Open Mathematics 6.3 (2008): 384-392. <http://eudml.org/doc/269275>.
@article{AllaDetinko2008,
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 \[ \mathbb \{F\} \]
×1q of GL(q, \[ \mathbb \{F\} \]
), such that G/\[ \mathbb \{F\} \]
×1q 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.},
author = {Alla Detinko, Dane Flannery},
journal = {Open Mathematics},
keywords = {linear group; periodic group; projective general linear group; field; classification; linear groups over finite fields; maximal irreducible periodic subgroups},
language = {eng},
number = {3},
pages = {384-392},
title = {Periodic subgroups of projective linear groups in positive characteristic},
url = {http://eudml.org/doc/269275},
volume = {6},
year = {2008},
}
TY - JOUR
AU - Alla Detinko
AU - Dane Flannery
TI - Periodic subgroups of projective linear groups in positive characteristic
JO - Open Mathematics
PY - 2008
VL - 6
IS - 3
SP - 384
EP - 392
AB - 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 \[ \mathbb {F} \]
×1q of GL(q, \[ \mathbb {F} \]
), such that G/\[ \mathbb {F} \]
×1q 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.
LA - eng
KW - linear group; periodic group; projective general linear group; field; classification; linear groups over finite fields; maximal irreducible periodic subgroups
UR - http://eudml.org/doc/269275
ER -
References
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