Question

Does the order of a finite group divide the product of degrees of a system of parameters of the invariant algebra?

score 35 · Answer 1 · 2026-03-26 19:39:37

35

Views

Does the order of a finite group divide the product of degrees of a system of parameters of the invariant algebra?

Published on 26 Mar 2026 - 19:39

score 28 · Answer 2 · 2016-02-07 19:01:24

28

Views

Why are two transitive actions of a group G equivalent if there exist an automorphism of G swapping two point stabilisers?

Published on 07 Feb 2016 - 19:01

score 139 · Answer 3 · 2016-02-08 22:26:11

139

Views

If $G$ acts $k$-transitive and $k > 5$ and $G$ is neither alternating nor symmetric, then $(n-k)! \ge 2n$

Published on 08 Feb 2016 - 22:26

score 59 · Answer 4 · 2016-02-10 22:37:09

59

Views

Does $X^{C_2} \simeq * \simeq X/{C_2}$ imply $X \simeq *$?

Published on 10 Feb 2016 - 22:37

score 48 · Answer 5 · 2016-02-13 17:01:57

48

Views

CG-homorphism proof. Stuck at the end!

Published on 13 Feb 2016 - 17:01

score 92 · Answer 6 · 2016-02-13 23:05:41

92

Views

Properly discontinuous action on hyperbolic plane

Published on 13 Feb 2016 - 23:05

score 61 · Answer 7 · 2016-02-14 12:25:38

61

Views

In permutation groups with trivial four-point stabilizers we have $N_G(N_G(M_0)) \le N_G(M_0)$ for $M_0 = G_{\alpha}\cap G_{\beta}\cap G_{\gamma}$.

Published on 14 Feb 2016 - 12:25

score 32 · Answer 8 · 2016-02-14 18:45:21

32

Views

If $e \in E$ where $E$ is a component of a permutation group, then $e$ has order $2$ or $3$ if $|\mbox{fix}(g)| \le 3$ for all nontrivial $g \in G$

Published on 14 Feb 2016 - 18:45

score 45 · Answer 9 · 2016-02-15 12:32:26

45

Views

In permutation group with $3$-group $H := G_{\alpha}$ and $|\mbox{fix}(H)| = 3$ and regular normal subgroup $N$, we have that $C_N(H)$ has even order

Published on 15 Feb 2016 - 12:32

score 49 · Answer 10 · 2016-02-15 18:32:06

49

Views

If $PSL_2(2^k)$ acts on odd set such that $|\mbox{fix}(g)|\le 3$ for $g\ne 1$, then $G_{\alpha}$ has element of order $\frac{q-1}{\gcd(q-1,3)}$

Published on 15 Feb 2016 - 18:32

score 49 · Answer 11 · 2016-02-16 12:18:13

49

Views

If $A_6$ acts on set of size $45$, then every involution fixes five points

Published on 16 Feb 2016 - 12:18

score 60 · Answer 12 · 2016-02-16 19:49:32

60

Views

If $H$ fixes three points, then could the normalizer of $H$ induce an orbit of size two on the fixed points

Published on 16 Feb 2016 - 19:49

score 125 · Answer 13 · 2016-02-18 15:51:39

125

Views

Group Action highly transitive

Published on 18 Feb 2016 - 15:51

score 646 · Answer 14 · 2026-03-29 19:10:53

646

Views

Symmetries of octahedron with $2$-faces action

Published on 29 Mar 2026 - 19:10

score 2.1k · Answer 15 · 2016-02-21 11:02:46

2.1k

Views

Groups Theory. Prove the intersection of stabilizer is exactly the kernel of the action.

Published on 21 Feb 2016 - 11:02

List Question

Does the order of a finite group divide the product of degrees of a system of parameters of the invariant algebra?

Why are two transitive actions of a group G equivalent if there exist an automorphism of G swapping two point stabilisers?

If $G$ acts $k$-transitive and $k > 5$ and $G$ is neither alternating nor symmetric, then $(n-k)! \ge 2n$

Does $X^{C_2} \simeq * \simeq X/{C_2}$ imply $X \simeq *$?

CG-homorphism proof. Stuck at the end!

Properly discontinuous action on hyperbolic plane

In permutation groups with trivial four-point stabilizers we have $N_G(N_G(M_0)) \le N_G(M_0)$ for $M_0 = G_{\alpha}\cap G_{\beta}\cap G_{\gamma}$.

If $e \in E$ where $E$ is a component of a permutation group, then $e$ has order $2$ or $3$ if $|\mbox{fix}(g)| \le 3$ for all nontrivial $g \in G$

In permutation group with $3$-group $H := G_{\alpha}$ and $|\mbox{fix}(H)| = 3$ and regular normal subgroup $N$, we have that $C_N(H)$ has even order

If $PSL_2(2^k)$ acts on odd set such that $|\mbox{fix}(g)|\le 3$ for $g\ne 1$, then $G_{\alpha}$ has element of order $\frac{q-1}{\gcd(q-1,3)}$

If $A_6$ acts on set of size $45$, then every involution fixes five points

If $H$ fixes three points, then could the normalizer of $H$ induce an orbit of size two on the fixed points

Group Action highly transitive

Symmetries of octahedron with $2$-faces action

Groups Theory. Prove the intersection of stabilizer is exactly the kernel of the action.

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