S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on...

7
Fromlasttmei G rotational Coneukton phony isometries of the icosahedron dodecahedron first counted 1Gt 60 G acts on 5 tetrahedra y c set whose ebbs are G 43 S5 shoved that all 3 cycles 5 cycles are in image Iq 3 cedes 45 cycles geunk Ang Sr Asc im g I Ast 60 Go find 116,1 9 is agate 60 and in q As Conjugacy G T enumerate all elements of G identity 2 triangular trees notate 120 around one 20 vertues sold symmetry 4724 edges 1800 not I breech pain of edges is

Transcript of S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on...

Page 1: S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on itself these 9 are theorbits 6mi if G is a ggrog C a cog class ma pi Iiii p I s

Fromlasttmei

G rotational Coneukton phonyisometries of

the icosahedrondodecahedron

firstcounted 1Gt 60

G acts on 5 tetrahedra yc set whoseebbs

are

G 43 S5

shoved that all 3 cycles5cycles are in

image Iq3 cedes 45

cycles geunk AngSr

Asc im g

IAst 60 Gofind116,1

9 is agate60

and in q As

ConjugacyG T

enumerateall elements of Gidentity 2

triangular treesnotate 120 around one

20

vertues sold symmetry 4724

edges 1800 not I breechpainofedges

is

Page 2: S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on itself these 9 are theorbits 6mi if G is a ggrog C a cog class ma pi Iiii p I s

if glx 7 then light hx hy

28 bizhghas b b aa b h au bechoose h eGot Haida 3 b

glad aa hgh44 1 4,9

6 be

formal observation toshow Gsimple

notice if NOG ne N n n

n'cN

n'run gngt ntas.mg 9if new thenthefull conj.ch

defefnmel

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Intl lol Intel GG

Page 3: S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on itself these 9 are theorbits 6mi if G is a ggrog C a cog class ma pi Iiii p I s

Tomodssylowtheaenf

if p IlGI p pine3 He G IHI p

Importantrole is threeplaced by pgaps

Def Ag group is greyG Kel p

sun

Digression p grays

clas.set7ilGltZCG1tElClCcajclasscaghelgage d size 7

Gets tag on itself these9 are theorbits

6mi if Gis ag grog

C a cogclass

ma piIiii

p I s KI

p l 1Gt Eld p IlHost

Page 4: S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on itself these 9 are theorbits 6mi if G is a ggrog C a cog class ma pi Iiii p I s

2 G e if G is a p gap

if G is a y group2 Cotte 2 Ca a G

can In Gzc

another p groupsmaller

2 Kaos e

the ascendingcentral sores f G

if G has a acgwhich exhausts

thespwe sq G is nilpotent

Appleton

if 1Gt p G I pG is Abelian

it gets gte then Sg te

kg 111Gt

Page 5: S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on itself these 9 are theorbits 6mi if G is a ggrog C a cog class ma pi Iiii p I s

Cgt G G Cp

161 15 LZCGII p.ph

if that pknow 2 G Sz e E zP

GonomIcants ZLotugzchug22to

LGtECGyl pcy

itgZCGnontrivial corset

G 4 giza gizi

z et 22 3

gizi glaze gigkzizlgitkzjxe

gkgizlzj.gl'Elgizi

Page 6: S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on itself these 9 are theorbits 6mi if G is a ggrog C a cog class ma pi Iiii p I s

glaze gize

Gtp G Aldrin

Agt8 Q Ltl ti It

2Cag It

0 8 2 10gV4

TheExtension problem

Guen N E gnayscan we classify

allgroups G contyN as a normal

stymysack that you EE

Answer is usuallyhorrible butoccasionally

beautiful

EasiestpassiblewayiProduct

Page 7: S5...G Kel p sun Digression pgrays clas.set7ilGl tZCG1tElClCcaj class caghelgage d size 7 Getstag on itself these 9 are theorbits 6mi if G is a ggrog C a cog class ma pi Iiii p I s

Did it G Gagoyns

G x Gz Cgi.ge gic GiB

gia.gDlgicgil Cg.g gaga

canst if gun N E then

G NAE cantans n.esneN3aGm4thatEEntaN