Question

Prove that the binomial coefficent $\binom{2p}{p} $ is $\equiv 2\pmod{p}$ using group actions.

score 118 · Answer 1 · 2015-10-31 14:11:21

118

Views

Prove that the binomial coefficent $\binom{2p}{p} $ is $\equiv 2\pmod{p}$ using group actions.

Published on 31 Oct 2015 - 14:11

score 623 · Answer 2 · 2015-10-31 17:21:51

623

Views

Group actions and cardinality of double cosets

Published on 31 Oct 2015 - 17:21

score 351 · Answer 3 · 2015-11-01 13:58:51

351

Views

Prove that if $G$ is finite, then any neighborhood of a $G$-invariant subset of $X$ contains a $G$- invariant neighborhood

Published on 01 Nov 2015 - 13:58

score 1.4k · Answer 4 · 2015-11-01 15:45:33

1.4k

Views

Commutator Group of $S_4$ and $A_4$

Published on 01 Nov 2015 - 15:45

score 239 · Answer 5 · 2026-02-23 10:07:15

239

Views

Group Action and stabilizer problem.

Published on 23 Feb 2026 - 10:07

score 60 · Answer 6 · 2015-11-02 07:35:05

60

Views

Group of order $p^n$ acting on a set of set of order $pm$

Published on 02 Nov 2015 - 7:35

score 36 · Answer 7 · 2015-11-03 13:52:06

36

Views

In a finite permutation group where $|\mbox{fix}(g)| \le 2$ for $g \ne 1$. Properties of orbit of $O_p(G)G_{\alpha}$.

Published on 03 Nov 2015 - 13:52

score 85 · Answer 8 · 2026-03-31 02:40:07

85

Views

Reasoning about subgroups $H \le PSL(2,q)$ based on knowledge about subgroups of normalizers in it

Published on 31 Mar 2026 - 2:40

score 95 · Answer 9 · 2015-11-05 10:50:26

95

Views

Let $G$ act such that each nontrivial element has at most two fixed point and $P := O_p(N)$. Then $G_{\alpha}$ acts fixed point freely on $P$

Published on 05 Nov 2015 - 10:50

score 128 · Answer 10 · 2015-11-05 22:34:50

128

Views

The centralizer of an involution in a permutation group where $|\mbox{fix}(g)| \le 2$ for $g \ne 1$

Published on 05 Nov 2015 - 22:34

score 25 · Answer 11 · 2015-11-06 22:53:23

25

Views

Direct caracterisation of certain subgroups of GL(E)

Published on 06 Nov 2015 - 22:53

score 115 · Answer 12 · 2026-02-23 06:00:36

115

Views

Averaging measurable functions over actions of amenable groups

Published on 23 Feb 2026 - 6:00

score 98 · Answer 13 · 2015-11-08 12:52:57

98

Views

The alternating group $A_7$ cannot act transitive, nonregular and such that $|\mbox{fix}(g)| \le 2$ for $g \ne 1$ on any finite set

Published on 08 Nov 2015 - 12:52

score 148 · Answer 14 · 2015-11-08 19:01:22

148

Views

Let $G$ act such that $|\mbox{fix}(g)| \le 2$ for $g \ne 1$. Then the Sylow $2$-subgroups acts regular on certain orbits

Published on 08 Nov 2015 - 19:01

score 254 · Answer 15 · 2015-11-09 17:52:48

254

Views

Show that for transitive subgroup $A$, its centralizer divides $|\Omega| = |A : A_{\alpha}|$

Published on 09 Nov 2015 - 17:52

List Question

Prove that the binomial coefficent $\binom{2p}{p} $ is $\equiv 2\pmod{p}$ using group actions.

Group actions and cardinality of double cosets

Prove that if $G$ is finite, then any neighborhood of a $G$-invariant subset of $X$ contains a $G$- invariant neighborhood

Commutator Group of $S_4$ and $A_4$

Group Action and stabilizer problem.

Group of order $p^n$ acting on a set of set of order $pm$

In a finite permutation group where $|\mbox{fix}(g)| \le 2$ for $g \ne 1$. Properties of orbit of $O_p(G)G_{\alpha}$.

Reasoning about subgroups $H \le PSL(2,q)$ based on knowledge about subgroups of normalizers in it

Let $G$ act such that each nontrivial element has at most two fixed point and $P := O_p(N)$. Then $G_{\alpha}$ acts fixed point freely on $P$

The centralizer of an involution in a permutation group where $|\mbox{fix}(g)| \le 2$ for $g \ne 1$

Direct caracterisation of certain subgroups of GL(E)

Averaging measurable functions over actions of amenable groups

The alternating group $A_7$ cannot act transitive, nonregular and such that $|\mbox{fix}(g)| \le 2$ for $g \ne 1$ on any finite set

Let $G$ act such that $|\mbox{fix}(g)| \le 2$ for $g \ne 1$. Then the Sylow $2$-subgroups acts regular on certain orbits

Show that for transitive subgroup $A$, its centralizer divides $|\Omega| = |A : A_{\alpha}|$

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