Periodic subgroups of projective linear groups in positive characteristic

• Autorzy: Alla Detinko , Dane Flannery
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

linear group; periodic group; projective general linear group; field; classification

Kategorie tematyczne

• 20Exx: Structure and classification of infinite or finite groups
• 20H20: Other matrix groups over fields

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 3
• Strony: 384-392

Daty

wydano

2008-09-01

online

2008-07-02

Twórcy

autor

Alla Detinko

• National University of Ireland

autor

Dane Flannery

• National University of Ireland

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-008-0033-9