Subgroups of the special linear group containing the diagonal subgroup (Q752185)

In the paper subgroups of the special linear group \(SL_ 2(K)\) of degree 2 over a field K, containing the subgroup D of all diagonal matrices are described. If char \(K\neq 2\), \(| K| >11\) and \(D<F\leq SL_ 2(K)\) then F is one of the following: the subgroup M of all monomial matrices, the subgroup U of upper triangular matrices, the subgroup L of all lower triangular matrices or \(SL_ 2(K)\) (Theorem 1). If char K\(=2\), \(K\neq GF(2)\) and \(D<F\leq SL_ 2(K)\) then one of the following occurs: \(F\leq U\), \(F\leq L\) or \(M\leq F\) (Theorem 2).