List questions from group-actions

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Finding the orbit of an element in $S_5$

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How can a set of fixed points be viewed as a $N_{G}(H)/H$ - set?

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Split a regular tetrahedron into four equal сonvex polyhedrons.

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Dummit Foote Exercise 1.7.10.a permutations of subsets self-study

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Trivial group action

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elaboration of group action definition.

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The Variety of 3-dimensional Real Lie Algebra Structures

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how did we know the action in $\mathbb{Z}_{11} \rtimes_{\varphi} \mathbb{Z}_{5}$?

Published on 28 Mar 2026 - 3:02

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Why any permutation defines an automorphism?

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If a finite group acts freely, then it acts properly discontinuously.

Published on 24 Oct 2020 - 13:52

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Isometry group of $\mathbb{Z}$

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Quotient of Hausdorff space by free discrete group action is Hausdorff

Published on 25 Oct 2020 - 9:00

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Why $SL_{n}(k)$ acts on $V$ by restriction?

Published on 31 Mar 2026 - 10:43

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A subalgebra $A(X)^G$ of $G$-invariant functions on $X$ is finitely generated subalgebra where $G$ is a finite group.

Published on 27 Mar 2026 - 2:36

List Question

About groups act faithfully on a set

Finding the orbit of an element in $S_5$

How can a set of fixed points be viewed as a $N_{G}(H)/H$ - set?

Split a regular tetrahedron into four equal сonvex polyhedrons.

Dummit Foote Exercise 1.7.10.a permutations of subsets self-study

Trivial group action

elaboration of group action definition.

The Variety of 3-dimensional Real Lie Algebra Structures

how did we know the action in $\mathbb{Z}_{11} \rtimes_{\varphi} \mathbb{Z}_{5}$?

Why any permutation defines an automorphism?

If a finite group acts freely, then it acts properly discontinuously.

Isometry group of $\mathbb{Z}$

Quotient of Hausdorff space by free discrete group action is Hausdorff

Why $SL_{n}(k)$ acts on $V$ by restriction?

A subalgebra $A(X)^G$ of $G$-invariant functions on $X$ is finitely generated subalgebra where $G$ is a finite group.

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