1) Let G = { e,a,b,c,d,f } be a group with identity element e and a Cayley Table
ID: 3101550 • Letter: 1
Question
1) Let G = { e,a,b,c,d,f } be a group with identity element e and a Cayley Table as shown below:
X
e
a
b
c
d
f
e
e
a
b
c
d
f
a
a
e
f
d
c
b
b
b
d
c
e
f
a
c
c
f
e
b
a
d
d
d
b
a
f
e
c
f
f
c
d
a
b
e
Use this Cayley Table to answer the following.
(a) = { }
(b) = { }
2) Find(3) in U (4): (3) = { }
3) Find(3) in U (5): (3) = { }
4) Find(3) in U (10): (3) = { }
X
e
a
b
c
d
f
e
e
a
b
c
d
f
a
a
e
f
d
c
b
b
b
d
c
e
f
a
c
c
f
e
b
a
d
d
d
b
a
f
e
c
f
f
c
d
a
b
e
Explanation / Answer
1) (a) is the set of the powers of a until you get to the identity,ei: (a)={e,a} Same thing for b (b)={e,b,c} 2) U4={1,3} so (3) in U4 is {1,3} U5={1,2,3,4} SO (3) in U5 is {1,3,4,2} because 3^0=1,3^1=3,3^2=9=4mod5, 3^3=27=2mod5, 3^4=71=1MOD5 so since you are back to the identity you should stop at 3^3. 4) you do the same thing as 3) ,
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