Title | FACTORIZATIONS OF THE GROUPS $\Omega_{7}(q)$ |
Publication Type | Journal Article |
Year of Publication | 1998 |
Authors | Gentcheva E, Gentchev T |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 90 |
Issue | Livre 1 - Mathématiques et Mecanique |
Pagination | 125-132 |
ISSN | 0205-0808 |
Keywords | factorizations of groups, Finite simple groups, groups of Lie type |
Abstract | The following result is proved: Let $G=\Omega_{7}(q)$ and $q$ is odd. Suppose that $G = AB$, where $A,B$ are proper non-Abelian simple subgroups of $G$. Then one of the following holds: (1) $q = 3 \textrm{ and } A \cong L_{4}(3) \textrm{ or } G_{2}(3), B \cong Sp_{6}(2) \textrm{ or } A_{9} ;$ (2) $q \equiv -1 \textrm{ (mod 4) and } A \cong G_{2}(q), B \cong L_{4}(q); $ (3) $q \equiv 1 \textrm{ (mod 4) and } A \cong G_{2}(q), B \cong U_{4}(q); $ (4) $q = 3^{2n+1} > 3 \textrm{ and } A \cong \text{ }^{2}G_{2}(q), B \cong L_{4}(q); $ (5) $q = 3^{2n+1} \textrm{ and } A \cong U_{3}(q), B \cong L_{4}(q); $ (6) $q = 3^{2n} \textrm{ and } A \cong L_{3}(q), B \cong U_{4}(q); $ (7) $A \cong G_{2}(q), B \cong PSp_{4}(q). $ |
1991/95 MSC | 20D06, 20D40, secondary 20G40 |
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