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
SN - 1895-1074
VL - 6
SP - 384
EP - 392
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
IS - 3
ER -