List questions from orbit-stabilizer

Published on 17 Jun 2022 - 6:45

40

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Computing the stabilizer of any polynomial of degree $n$ with distinct roots.

Published on 30 Jul 2022 - 13:39

193

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How to Find Orbits and Stabilizers

Published on 10 Aug 2022 - 9:53

59

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Let $G$ be a group with $25$ elements and $E$ a $G$-set with $32$ elements. Show that there exists $a \in E$ such that $G_a=G$.

Published on 12 Aug 2022 - 9:22

178

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$G$ acts transitively on a set $X$, where $|X|=m\in\mathbb{Z}_{>0}$, if and only if there exsits $H\leq G$ with index $m$.

Published on 04 Sep 2022 - 10:17

137

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Showing $gG_ag^{-1}=G_{ga}$

Published on 19 Sep 2022 - 3:57

208

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Questioning the relationship between the orbit-stabilizer theorem and Lagrange's theorem

Published on 20 Sep 2022 - 15:55

60

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intersection of point stabilisers is trivial

Published on 23 Feb 2026 - 6:37

53

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Why do we require $X$ to be a finite set when we count $|X|$ via orbits?

Published on 15 Oct 2022 - 23:02

57

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Point stabilizer subgroups of permutation groups of order $p^aq^b$?

Published on 17 Oct 2022 - 17:40

599

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Simply transitive action and $G$-isomorphism.

Published on 17 Oct 2022 - 22:50

134

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Stabiliser group

Published on 23 Feb 2026 - 6:33

63

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Burnside’s Lemma for a triangle (group action clarification)

Published on 30 Nov 2022 - 15:31

56

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Prove that $\mathrm{Ind}_{H}^{G}(U) \cong \mathbb{C}X$ as $G$-reps where $X$ is transitive, $H = G_x$, $U$ is the trivial $H$-rep

Published on 08 Dec 2022 - 20:50

List Question

Orbits of a matrix group

Computing the stabilizer of any polynomial of degree $n$ with distinct roots.

How to Find Orbits and Stabilizers

Let $G$ be a group with $25$ elements and $E$ a $G$-set with $32$ elements. Show that there exists $a \in E$ such that $G_a=G$.

$G$ acts transitively on a set $X$, where $|X|=m\in\mathbb{Z}_{>0}$, if and only if there exsits $H\leq G$ with index $m$.

Showing $gG_ag^{-1}=G_{ga}$

Questioning the relationship between the orbit-stabilizer theorem and Lagrange's theorem

intersection of point stabilisers is trivial

Why do we require $X$ to be a finite set when we count $|X|$ via orbits?

Point stabilizer subgroups of permutation groups of order $p^aq^b$?

Simply transitive action and $G$-isomorphism.

Stabiliser group

Burnside’s Lemma for a triangle (group action clarification)

Prove that $\mathrm{Ind}_{H}^{G}(U) \cong \mathbb{C}X$ as $G$-reps where $X$ is transitive, $H = G_x$, $U$ is the trivial $H$-rep

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