This preview shows page 1. Sign up to view the full content.
MATH 113  S2
MIDTERM 2
1
(4 pts) Compute the order of (3
,
4) in the group
Z
9
×
Z
30
.
2
Let
σ
=
±
1 2 3 4 5 6 7 8
2 4 1 6 8 3 7 5
²
a
(3 pts) Write
σ
as a product of disjoint cycles.
b
(3 pts) Hence write sigma as a product of transpositions, and determine whether
σ
is an even permutation.
3
(5 pts) Let
φ
:
G
→
G
0
be a
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: surjective homomorphism. Assume G is abelian. Show that G is also abelian. 4 (5 pts) Let φ : G → G be a surjective homomorphism . Assume that G is ﬁnite. Show that  G  =  G  ×  ker φ  (Hint: use the fundamental homomorphism theorem.) 1...
View
Full
Document
This note was uploaded on 06/15/2009 for the course MATH 113 taught by Professor Ogus during the Fall '08 term at University of California, Berkeley.
 Fall '08
 OGUS
 Math, Algebra

Click to edit the document details