The exercise is from the book by Alperin 'Groups and Representations' If $B$ is the usual Borel subgroup of $GL(n,F)$. Determine all the the subgroups of $SL(n,F)$ which contain $B\cap SL(n,F)$.

So $B$- consists of all invertible upper triangular matrices. $SL(n,F)$- special linear subgroup that consist of all marices with determinant equal to 1. Hence $B\cap SL(n,F)$ is the set of all triangular invertible matrices with determinant equal to 1.

How do I determine subgroups of $SL(n,F)$ which contain that kind of matrices?


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