PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Open Mathematics

2008 | 6 | 3 | 384-392
Tytuł artykułu

### Periodic subgroups of projective linear groups in positive characteristic

Autorzy
Treść / Zawartość
Warianty tytułu
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
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
384-392
Opis fizyczny
Daty
wydano
2008-09-01
online
2008-07-02
Twórcy
autor
autor
Bibliografia
• [1] Bácskai Z., Finite irreducible monomial groups of small prime degree, Ph.D. thesis, Australian National University, 1999
• [2] Detinko A.S., Maximal periodic subgroups of classical groups over fields of positive characteristic I, Vestsi Akad. Navuk BSSR Ser. Fiz.-Mat., 1993, 4, 35–39 (in Russian)
• [3] Detinko A.S., Maximal periodic subgroups of classical groups over fields of positive characteristic II, Vestsi Akad. Navuk BSSR Ser. Fiz.-Mat., 1994, 2, 49–52 (in Russian)
• [4] Detinko A.S., On deciding finiteness for matrix groups over fields of positive characteristic, LMS J. Comput. Math., 2001, 4, 64–72
• [5] Dixon J.D., Zalesskii A.E., Finite primitive linear groups of prime degree, J. London Math. Soc., 1998, 57, 126–134 http://dx.doi.org/10.1112/S0024610798005778
• [6] Dixon J.D., Zalesskii A.E., Finite imprimitive linear groups of prime degree, J. Algebra, 2004, 276, 340–370 http://dx.doi.org/10.1016/j.jalgebra.2004.02.005
• [7] Flannery D.L., Detinko A.S., Locally nilpotent linear groups, Irish Math. Soc. Bull., 2005, 56, 37–51
• [8] Isaacs I.M., Character theory of finite groups, Dover Publications, Inc., New York, 1994
• [9] Konyukh V.S., Metabelian subgroups of the general linear group over an arbitrary field, Dokl. Akad. Nauk BSSR, 1978, 22, 389–392 (in Russian)
• [10] Konyukh V.S., Sylow p-subgroups of a projective linear group, Vestsi Akad. Navuk BSSR Ser. Fiz.-Mat., 1985, 6, 23–29 (in Russian)
• [11] Mazurova V.N., Maximal periodic subgroups of a symplectic group, Dokl. Akad. Nauk BSSR, 1985, 29, 403–406 (in Russian)
• [12] Mazurova V.N., Periodic subgroups of classical groups over fields of positive characteristic, Dokl. Akad. Nauk BSSR, 1985, 29, 493–496 (in Russian)
• [13] Suprunenko D.A., Matrix groups, Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, 1976, 45
• [14] Wehrfritz B.A.F., Infinite linear groups, Springer-Verlag, Berlin, Heidelberg, New York, 1973
• [15] Winter D.J., Representations of locally finite groups, Bull. Amer. Math. Soc., 1968, 74, 145–148 http://dx.doi.org/10.1090/S0002-9904-1968-11913-5
• [16] Zalesskii A.E., Maximal periodic subgroups of the full linear group over a field with positive characteristic, Vesci Akad. Navuk BSSR Ser. Fiz.-Mat. Navuk, 1966, 2, 121–123 (in Russian)
• [17] Zalesskii A.E., Mazurova V.N., Maximal periodic subgroups of the orthogonal group, Institute of Mathematics AN BSSR, 1985, 9, 218 (in Russian)
Typ dokumentu
Bibliografia
Identyfikatory