Affiliation:
1. Dipartimento di Matematica e Fisica , Università Cattolica del Sacro Cuore , Via della Garzetta 48, 25133 Brescia , Italy
Abstract
Abstract
We construct
(
2
,
3
)
(2,3)
-generators for the finite 8-dimensional orthogonal groups, proving the following results: the groups
Ω
8
+
(
q
)
\Omega_{8}^{+}(q)
and
P
Ω
8
+
(
q
)
\mathrm{P}\Omega_{8}^{+}(q)
are
(
2
,
3
)
(2,3)
-generated if and only if
q
≥
4
q\geq 4
; the groups
Ω
8
-
(
q
)
\Omega_{8}^{-}(q)
and
P
Ω
8
-
(
q
)
\mathrm{P}\Omega_{8}^{-}(q)
are
(
2
,
3
)
(2,3)
-generated for all
q
≥
2
q\geq 2
.
Subject
Algebra and Number Theory
Reference15 articles.
1. J. N. Bray, D. F. Holt and C. M. Roney-Dougal,
The Maximal Subgroups of the Low-Dimensional Finite Classical Groups,
London Math. Soc. Lecture Note Ser. 407,
Cambridge University, Cambridge, 2013.
2. L. Carlitz,
A theorem of Dickson on irreducible polynomials,
Proc. Amer. Math. Soc. 3 (1952), 693–700.
3. R. W. Carter,
Simple Groups of Lie Type,
John Wiley & Sons, New York, 1972.
4. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson,
Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups,
Oxford University, Eynsham, 1985.
5. N. Jacobson,
Basic Algebra. I, 2nd ed.,
W.H. Freeman, New York, 1985.