# 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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