VII. Group Actions Flashcards
1
Q
Definition
Left and right actions.
A
2
Q
Lemma VII.1.5
Equivalence relation under actions.
A
3
Q
Definition
Orbit.
Fixed point and set of fixed points.
A
4
Q
Lemma VII.1.6
The set of orbits…
A
5
Q
Definition
Transitive action, iff.
A
6
Q
Definition
Stabiliser.
A
7
Q
Lemma VII.1.13
Stab_{G}(x) is….
Moreover, Stab_{G}(x) = G iff.
A
8
Q
Theorem VII.1.16
Orbit-stabiliser Theorem.
A
9
Q
Lemma VII.2.1
If p prime and C_{p} acts on x, then…
A
10
Q
Lemma VII.2.2
If G finite and p prime…
A
11
Q
Theorem VII.2.3
Cauchy’s Theorem.
A
12
Q
Definition
Conjugates.
A
13
Q
Theorem VII.3.2
G acts on itself…
A
14
Q
Definition
Conjugacy class.
Centraliser.
A
15
Q
Definition
Cycle type.
A
