Permutation gzu.
grus
Permitation on a det! A namulalin
6:A A
ijei
fn)Pamtalion grp s4 A:A t of yamulaliona an A wthih for
wnde function
Set
denetad a S(A)
Thm Let paA lee a set (SIA), ) a
a guop
So, foh:AA
fohiH and onto
Sacondly, aeialnty
Th ideadtaty the idenly functiom I: A’A
Tof -foI -j Vfe SA)
, s(23)
n=3
n3 for
Aean hon-
3
4 |
4 3 2 1 4 |23
3jJ 43
4l2
conyoritan
cnly 4 3
matn Zn
Notain Matn
i’2
Ezamples
A-,2,,n3 Let
(sa),)
QED
fof'=fof
I -
eSA)
lajection H
a since
SA) fe Gin 4
Date:
No. Page E
, Date:
mean
n)
2,., ib called the Aymain grop 4
S, =Sit,
Sal= n!
6 2
60) 62) 6a)
nchaiey (n)chsues I choie
S,l=n!
Sy has asad 3o Agus
S has aund
Cyele notalin Cyce reentalion a nemtain
y=l23 47 iD the sane as y= l342)
|3 4 2
E- () (2) B)
q= ((23)
at=(132) -Cydes unl be
as = V2) (3)
a'g (13)2) =(L3)
= (2) dorypad
B= )(23) = 23)
, |Page No.
Date:
Examples Q= [L23 45
4 6 ’ &= (2 )(346)
l2 1 4 653
I3
2 36 2 ) - 1 s23)(44)
4S6
5 4
eß =(5) (243)
(o5-o6-2o24)
fA-L2,,nj Then, SIA) =Sncalled the ynnátni
n S,l n!
t,2,3)- (123) Commas
dopped.
# Cyde s ngthn has ode n
Dekinion la, a a peemutedion cyde ntain
then n-ye
a= (3) (27)(456) (B) ?
p= (1237) (b46) (5)
&ß = (1732)(48)(s6)
(13) (27) (us6) C8) (1232) (6n3) (s)
B = (23) (6M6) (s ) Us) 7) (us) (& J
732)(45) (68)
grus
Permitation on a det! A namulalin
6:A A
ijei
fn)Pamtalion grp s4 A:A t of yamulaliona an A wthih for
wnde function
Set
denetad a S(A)
Thm Let paA lee a set (SIA), ) a
a guop
So, foh:AA
fohiH and onto
Sacondly, aeialnty
Th ideadtaty the idenly functiom I: A’A
Tof -foI -j Vfe SA)
, s(23)
n=3
n3 for
Aean hon-
3
4 |
4 3 2 1 4 |23
3jJ 43
4l2
conyoritan
cnly 4 3
matn Zn
Notain Matn
i’2
Ezamples
A-,2,,n3 Let
(sa),)
QED
fof'=fof
I -
eSA)
lajection H
a since
SA) fe Gin 4
Date:
No. Page E
, Date:
mean
n)
2,., ib called the Aymain grop 4
S, =Sit,
Sal= n!
6 2
60) 62) 6a)
nchaiey (n)chsues I choie
S,l=n!
Sy has asad 3o Agus
S has aund
Cyele notalin Cyce reentalion a nemtain
y=l23 47 iD the sane as y= l342)
|3 4 2
E- () (2) B)
q= ((23)
at=(132) -Cydes unl be
as = V2) (3)
a'g (13)2) =(L3)
= (2) dorypad
B= )(23) = 23)
, |Page No.
Date:
Examples Q= [L23 45
4 6 ’ &= (2 )(346)
l2 1 4 653
I3
2 36 2 ) - 1 s23)(44)
4S6
5 4
eß =(5) (243)
(o5-o6-2o24)
fA-L2,,nj Then, SIA) =Sncalled the ynnátni
n S,l n!
t,2,3)- (123) Commas
dopped.
# Cyde s ngthn has ode n
Dekinion la, a a peemutedion cyde ntain
then n-ye
a= (3) (27)(456) (B) ?
p= (1237) (b46) (5)
&ß = (1732)(48)(s6)
(13) (27) (us6) C8) (1232) (6n3) (s)
B = (23) (6M6) (s ) Us) 7) (us) (& J
732)(45) (68)
