List questions from general-linear-group

Published on 18 Nov 2021 - 23:37

186

Views

When is the set of all upper triangular matrices in $\text{GL}(2, \mathbb{Z}/p \mathbb{Z})$ is abelian?

Published on 23 Nov 2021 - 12:05

69

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Maximal order with primitive determinant in $\operatorname{GL}_n(\mathbb{F}_q)$

Published on 29 Nov 2021 - 16:18

101

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Explicit construction of polynomial representation of $GL(n,\mathbb{R})$

Published on 30 Nov 2021 - 19:13

299

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Finding the order of an element in $GL(2,\mathbb F_p)$.

Published on 12 Jan 2022 - 5:47

38

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Order of completely reducible group action

Published on 12 Jan 2022 - 16:50

368

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Orbits of the action of $SL(n,\mathbb R)$ on $\mathbb R^n$.

Published on 20 Jan 2022 - 13:25

699

Views

Show that the general linear group $GL(n, \Bbb R)$ is a Lie group under matrix multiplication.

Published on 04 Feb 2022 - 20:50

85

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$GL_n(\mathbb{Z}_{pq})$ isomorphic to $GL_n(\mathbb{Z}_{p})\times GL_n(\mathbb{Z}_{q})$

Published on 10 Feb 2022 - 11:58

38

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Matrix and Groups Question Solution Check

Published on 23 Feb 2022 - 23:35

113

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When is it possible to find an invertible matrix of order $n+1$

Published on 01 Mar 2022 - 21:58

45

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Existence of $n\times n$ invertible matrix of order $n+1$

Published on 03 Mar 2022 - 20:30

41

Views

Existence of a transvection which maps one hyperplane to another.

Published on 09 Mar 2022 - 8:03

180

Views

Find all subgroups of $\mathrm{GL}(2,\mathbf{R})$ of index 2.

Published on 25 Mar 2026 - 14:44

168

Views

The general linear group $GL(n, \mathbb{C})$ has no proper subgroup of finite index.

Published on 25 Mar 2026 - 0:33

List Question

p-subgroup of $\mathrm{GL}_{n}(\mathbb{F }_{p})$ and Sylow's Theorem

When is the set of all upper triangular matrices in $\text{GL}(2, \mathbb{Z}/p \mathbb{Z})$ is abelian?

Maximal order with primitive determinant in $\operatorname{GL}_n(\mathbb{F}_q)$

Explicit construction of polynomial representation of $GL(n,\mathbb{R})$

Finding the order of an element in $GL(2,\mathbb F_p)$.

Order of completely reducible group action

Orbits of the action of $SL(n,\mathbb R)$ on $\mathbb R^n$.

Show that the general linear group $GL(n, \Bbb R)$ is a Lie group under matrix multiplication.

$GL_n(\mathbb{Z}_{pq})$ isomorphic to $GL_n(\mathbb{Z}_{p})\times GL_n(\mathbb{Z}_{q})$

Matrix and Groups Question Solution Check

When is it possible to find an invertible matrix of order $n+1$

Existence of $n\times n$ invertible matrix of order $n+1$

Existence of a transvection which maps one hyperplane to another.

Find all subgroups of $\mathrm{GL}(2,\mathbf{R})$ of index 2.

The general linear group $GL(n, \mathbb{C})$ has no proper subgroup of finite index.

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