Question

Notions of groups acting on groups

score 648 · Answer 1 · 2016-01-09 10:36:19

648

Views

Notions of groups acting on groups

Published on 09 Jan 2016 - 10:36

score 480 · Answer 2 · 2016-01-09 20:03:43

480

Views

If $N_G(U) = TU$ for $T = \langle t \rangle$ with involution $t$, and $N \cap U \ne 1$, then $G = TUN$ and $UN$ is Frobenius group

Published on 09 Jan 2016 - 20:03

score 122 · Answer 3 · 2016-01-12 07:00:34

122

Views

Why is this a group action - what is the significance of $g^{-1}$?

Published on 12 Jan 2016 - 7:00

score 28 · Answer 4 · 2016-01-12 21:17:34

28

Views

If $G_{\alpha} \cong A_4$ and $|\mbox{fix}(g)| \in \{0,3\}$ for $g \ne 1$ and $V \le G_{\alpha}$ is the four-group in $A_4$, then $C_G(V) = V$

Published on 12 Jan 2016 - 21:17

score 713 · Answer 5 · 2016-01-13 04:09:51

713

Views

Transitive action on a finite set and group

Published on 13 Jan 2016 - 4:09

score 65 · Answer 6 · 2026-03-26 17:53:30

65

Views

Given $\pi:X\rightarrow Y$ how to show $X$ is irreducible (resp. normal) $\Rightarrow$ $Y$ is irreducible(resp. normal)?

Published on 26 Mar 2026 - 17:53

score 180 · Answer 7 · 2016-01-13 10:38:10

180

Views

Example in which a normal subgroup acts non-equivalent on its orbits

Published on 13 Jan 2016 - 10:38

score 60 · Answer 8 · 2016-01-13 15:01:05

60

Views

Two actions that should be non-equivalent on $A_4$, but they seem to be equivalent?

Published on 13 Jan 2016 - 15:01

score 663 · Answer 9 · 2016-01-13 16:10:25

663

Views

Significance of the notion of equivalent actions vs. permutation isomorphic action

Published on 13 Jan 2016 - 16:10

score 93 · Answer 10 · 2016-01-14 12:39:57

93

Views

If $G_{\alpha} \cong S_4$ and $|\mbox{fix}(g)| \in \{0,3\}$ for $g \ne 1$. Then $G$ has transitive normal subgroup of index $2$.

Published on 14 Jan 2016 - 12:39

score 56 · Answer 11 · 2016-01-14 16:42:32

56

Views

A subtle error in a "change of variable" in a sum

Published on 14 Jan 2016 - 16:42

score 637 · Answer 12 · 2016-01-15 00:47:37

637

Views

Groups of prime power and the fixed point set

Published on 15 Jan 2016 - 0:47

score 312 · Answer 13 · 2016-01-15 09:58:00

312

Views

If $G = VN$, $V$ a four group and $N$ regular normal, then there exists some Sylow subgroup left invariant by $V$

Published on 15 Jan 2016 - 9:58

score 96 · Answer 14 · 2016-01-15 14:08:48

96

Views

Show that $|C_G(u)| = 12$ by "counting involutions"

Published on 15 Jan 2016 - 14:08

score 106 · Answer 15 · 2016-01-16 19:41:37

106

Views

List Question

Notions of groups acting on groups

If $N_G(U) = TU$ for $T = \langle t \rangle$ with involution $t$, and $N \cap U \ne 1$, then $G = TUN$ and $UN$ is Frobenius group

Why is this a group action - what is the significance of $g^{-1}$?

If $G_{\alpha} \cong A_4$ and $|\mbox{fix}(g)| \in \{0,3\}$ for $g \ne 1$ and $V \le G_{\alpha}$ is the four-group in $A_4$, then $C_G(V) = V$

Transitive action on a finite set and group

Given $\pi:X\rightarrow Y$ how to show $X$ is irreducible (resp. normal) $\Rightarrow$ $Y$ is irreducible(resp. normal)?

Example in which a normal subgroup acts non-equivalent on its orbits

Two actions that should be non-equivalent on $A_4$, but they seem to be equivalent?

Significance of the notion of equivalent actions vs. permutation isomorphic action

If $G_{\alpha} \cong S_4$ and $|\mbox{fix}(g)| \in \{0,3\}$ for $g \ne 1$. Then $G$ has transitive normal subgroup of index $2$.

A subtle error in a "change of variable" in a sum

Groups of prime power and the fixed point set

If $G = VN$, $V$ a four group and $N$ regular normal, then there exists some Sylow subgroup left invariant by $V$

Show that $|C_G(u)| = 12$ by "counting involutions"

More question on the proof of orbit-stabilizer theorem from Gowers's weblog

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