# Questions tagged [linear-groups]

A linear group or matrix group is a group $G$ whose elements are invertible $n \times n$ matrices over a field $F$.

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### What is the maximal $m$, such that $\mathbb{Z}_2^m \leq GL(n, 2)$?

Is there any closed formula for the function $m(n)$, that is defined as the maximal $m$, such that there is $GL(n, 2)$ has a subgroup isomorphic to $\mathbb{Z}_2^m$? The only things I know currently, ...
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### Iwasawa Matrix Decomposition Proof

Iwasawa Decomposition (special case): Let $G=SL_n(\Bbb{R})$, $K=$ real unitary matrices, $U=$ upper triangular matrices with $1$'s on the diagonal (called unipotent), and $A=$ diagonal matrices with ...
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### References for (especially two-dimensional) general linear groups over *finite* fields

Questions. What are good, citable, detailed sources on general linear groups over finite fields? Especially, $\mathrm{GL}_2(\mathbb{F}_p)$, and most especially, the following: characterization of ...
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