Name:
Fall 2011
Math 3306 - Test 1
Date: l ' ( ~0 cfw_ 1\
An d cfw_ "0v\ ( _ roJ ~ ed
1. ( to Pts) Let S = cfw_ I, 2, 3 ,4 , 5 ,6,7,8,9, 10. o f each o f the following types o f mappings,
provide justification for why the example satisfies the conditions.
Math 3306
Wednesday, September 07, 2011
9:27 AM
Math 3306 Page 1
Associative law an operation on a set S is said to be associative if it satisfies the condition
a (b c) = (a b) c
Math 3306 Page 2
a (b c) = (a b) c
for all a, b, c S.
Identity - an element
Ch 4.16 Cosets
Tuesday, November 08, 2011
7:59 PM
Reminders:
modn is an equivalence relation on Z, the group of integers
For n Z+, if a Z, then [a] = cfw_b: a bmodn = cfw_b: a B is a multiple of n
For n Z+, cfw_[0], [1], [2],[n-1] is a partition of Z
Generators & Direct Products
Wednesday, November 02, 2011
9:36 AM
If G is a group and a in G we know what about <a> ?
In this section one objective is to generalize this idea of generating a group.
Theorem 15.1 If C denotes any collection of subgroups of
M ath 3 306 Test 2 Fall 2 011
1.
(10 points) True o r Falsi
~ or False .jn ~ ,
i.
( 1234 5) = ( 15) (14) ( 13) ( 12).
Sil1 (.L
.
( I 2- '5 ):- ( , 5 ) (/
U<t, (12 5) is an odd p ermutation .
z .)
ii.
True o @
iii .
True or~ , ~x ach positive integer