Periodic subgroups of projective linear groups in positive characteristic

Alla S. Detinko; Dane L. Flannery

doi:10.2478/s11533-008-0033-9

Periodic subgroups of projective linear groups in positive characteristic

Research output: Contribution to journal › Article › peer-review

Abstract

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^× 1_q of GL(q, F), such that G/F^×1_q 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 language	English
Pages (from-to)	384-392
Number of pages	9
Journal	Central European Journal of Mathematics
Volume	6
Issue number	3
Early online date	18 Jun 2008
DOIs	https://doi.org/10.2478/s11533-008-0033-9
Publication status	Published - 1 Sep 2008
Externally published	Yes

Access to Document

10.2478/s11533-008-0033-9Licence: Unspecified

Cite this

@article{82dfc73777a34fb1bdf5f1ebc836b1a8,

title = "Periodic subgroups of projective linear groups in positive characteristic",

abstract = "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.",

keywords = "Classification, Field, Linear group, Periodic group, Projective general linear group",

author = "Detinko, {Alla S.} and Flannery, {Dane L.}",

note = "Funding Information: This paper has emanated from research conducted with the financial support of Science Foundation Ireland, grant RFP05/MAT0008. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",

year = "2008",

month = sep,

day = "1",

doi = "10.2478/s11533-008-0033-9",

language = "English",

volume = "6",

pages = "384--392",

journal = "Open Mathematics",

issn = "1895-1074",

publisher = "Walter de Gruyter GmbH & Co. KG",

number = "3",

}

TY - JOUR

T1 - Periodic subgroups of projective linear groups in positive characteristic

AU - Detinko, Alla S.

AU - Flannery, Dane L.

N1 - Funding Information: This paper has emanated from research conducted with the financial support of Science Foundation Ireland, grant RFP05/MAT0008. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2008/9/1

Y1 - 2008/9/1

N2 - 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.

AB - 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.

KW - Classification

KW - Field

KW - Linear group

KW - Periodic group

KW - Projective general linear group

UR - http://www.scopus.com/inward/record.url?scp=47349122694&partnerID=8YFLogxK

U2 - 10.2478/s11533-008-0033-9

DO - 10.2478/s11533-008-0033-9

M3 - Article

AN - SCOPUS:47349122694

VL - 6

SP - 384

EP - 392

JO - Open Mathematics

JF - Open Mathematics

SN - 1895-1074

IS - 3

ER -

Periodic subgroups of projective linear groups in positive characteristic

Abstract

Access to Document

Other files and links

Fingerprint

Cite this