IV. Homomorphisms and Normal Subgroups Flashcards
1
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Definition
Conjugate.
Normal subgroup.
A
2
Q
Lemma IV.1.3
Equivalences to Normal subgroup.
A
3
Q
Lemma IV.1.8
If H subgroup of index 2.
A
4
Q
Definition
The set of left cosets.
If H is normal?
A
5
Q
Lemma IV.2.1
If N is Normal, then group operation on quotient group is well-defined.
Proof
A
6
Q
Lemma IV.2.2
If N Normal, then G/N
A
7
Q
Definition
Group homomorphism.
A
8
Q
Definition
Group isomorphism.
Kernel, image.
A
9
Q
Theorem IV.5.1
How do Ker and Im relate to G and H?
A
10
Q
Lemma IV.5.4
If \phi is a homom., \phi is injective iff.
A
11
Q
Theorem IV.6.1
The First Isomorphism Theorem
A
12
Q
Definition
sign(\sigma) is a homomorphism…
A
13
Q
Theorem IV.7.2
A_n and S_n
A
14
Q
Lemma IV.8.1
If G, H are cyclic of order…
A
15
Q
Lemma IV.8.4
If p prime, then any group of order p…
A
