zbMATH — the first resource for mathematics

The linear groups of small degree over the field of order 2. (Russian) Zbl 0617.20022
The author gives a complete list of the irreducible subgroups H of the group \(GL_{10}(2)\) provided all simple factors of H are known simple groups. In particular the list contains the following simple groups: \(L_ 5(4)\), \(U_ 5(2)\), \(L_ 2(11)\), \(L_ 2(32)\), \(L_ 5(2)\), \(\Omega^{\mp}_{10}(2)\), \(Sp_{10}(2)\), \(M_{11}\), \(M_{12}\), \(M_{22}.\)
Remark. Kleidman’s thesis (Cambridge Univ., 1986) contains a list of maximal subgroups of \(SL_ n(q)\) (n\(\leq 11)\) for all q.
Reviewer: A.Zalesskij

20G40 Linear algebraic groups over finite fields
20D05 Finite simple groups and their classification
20D30 Series and lattices of subgroups
Full Text: EuDML