<

Philip Hall Lecture Notes on Group Theory – Part VI

Dublin Core

Title

Philip Hall Lecture Notes on Group Theory – Part VI

Subject

Hall, Philip, 1904-1982

Description

This material is a set of unpublished, hand-written lecture notes composed by Philip Hall (1904-1982). They were written in the 1960s at the University of Cambridge, where Hall was a professor at King’s College.

Part VI


§6 Consequences of Sylow's Theorem. Pronormal Subgroups. Nilpotent Groups. (pp. 37-43)

Creator

Hall, Philip, 1904-1982

Source

The pages belong to Edward Spitznagel, Washington University Professor of Mathematics, and are xerographic reproductions made from originals held by (and with permission of) John G. Thompson, a contemporary and correspondent of Hall.

Date

1951-1967

Rights

Washington University asserts no copyright over digital reproductions of this material, and cannot give permission to use the materials or otherwise grant any exclusive rights of the copyright holder. It is your responsibility to assure that your use of the materials is permitted under applicable law.

PDF Search

Text

· ~ ,~~ ~~....G

1/

~ ,~ ~.

L~--~ ~·2.
Lee K Jc, "'" s~ 7 G- ~-~H. If H~GIk- H .sfn.. I< . S~-..~ f ~ /''""-- , olsn , ,J,,.. .,..J <J .:.V p~~ "J- sis,
~ u.

cL.-..r- ~"~ -{rr

sfn..

~ ~J-

.J

C40-C.

~ ~ sfJ;., /4

sf-~Jil-C ~u.J_t :

Le-.~ ~·3 fiJ
?-G- .~

L¢- H s~ K -::: .G-

If

H s~ 1<.

(iiiJ

'I

H -:: r. J-1 >.
.\ E-1\

f~; (i) . LJ..
1'\

H, _1

(!i) ~

<J

I')

c~r--.

k.t~
~

L

Qli)

H n /<..

sin.

"-~

~s .s~

I.e.

H-= H0

~~

~ ' i = I~
~

2..., ·--

{i l ~

~r

1-1 n I<

tL- H sfn. b-.

<t H, -<t • -~ <3

L(1- ..3·'+ a....)
slww IW;- H

a

s*~

B(J

G-.

"'

Hr-=- I<.
Ln H s~ L n I<

So

~·!,_ G- -.J I< sin. 6

s"-'- H,... G- = H

ta.J

It;.. ~

So

ii) .

(.B) .

S~fvu. IW 7-=- iH) H'~j

a. · ;- fr""'t

it'

H ;h\, G-.
S· 2. (jv)



H .s~ T .

~o.., H

<1

':r

T

8:1 6 ..:z

&·I .;

>

~ j

E:

~

G

H ;~ 7.

B;r

~CL-

4oo.J .so H -=Hi

:r.

H- -,~

Cn~~ ;)
~A.~J

~

l..t

H

.fnt~UL ~~

~"-!~ "(/ H

B:y

S·ll- Liii) ,

~

S,

~

L

K. .s.l,.. L ~ ~ H .rl,.. L .·
""'l 4Z~ H, .s~ G- ,

~

{.r
It

H.:



s~ L n I<.

L"' H

(ji )

L

a..ll

~ G-

,;

H ~ T ~

,._ -..

p-.t-Ls""""r '1 G-. B:~

r- .S~o-t'

s

"f t;...

~~ ~ S.

s, ,

~

T i.

7L.o
·-·--·--

./..,.,A..

"~

ko

JLr

4..

'c.r-

fJ~ ;-.r~

6 S·~ (!iV
3

~ S,

a...e.

1-

T

w (ji J, ~
~~..);, ..:. .G .

'if ~"'!~ "/- H ~ b-- •
BJ. l:Jp~ .:. , /1.;, ~"'~' ~ ~~. ~u. H 'f'l =- H -41 H ~
~j~~ I. H.x_ ~ . ;r. S~ _. r ~ - a.rl,;J-("7L7 , H ;~ 6-. -·~--- _

l j S·lf- (;i) ,

c..J~ lie,

s...,,~ ltJ:

i.

L.et 7={H, H~J ~ !~. G- -.

.;. "'- f:J~ ;-s~ -1 G-.
At,"
H 1" ~ T
~ .ro--c.t~- ? E ;r. S~ S
.~

S·lt- Cf.ii) , H

~ ~ . ,~

--·--- -- - -

~

r

~

'1-

LJ:

6·4

.f -e.t\.cl...

H

k

~ ;-~~

'1

G-.

s,~ ;·s~f-j-G- ~~

"1-

~ H fht, G-

.svto..4

~

a.J

f ~ ~'"1--~

H ~ &.

~ 1' IE o-fo..;..._ H > ~ .s-J-~ ~ <xt~ L~ .r~ lt..t
H ~ ~ ~ ~ 7' ...nAt H!.6fr-cl lr G- . 71..~ .w I~ LJ..J,.,.Jt

~~ ; 6.....t Lz.~ ~ sLJL "~~ s~ fJ ,;. ;~~ ~ G-.
~ (,·ft. I
lj H ~ '£ ~ P k ~ S!l~ ;-s~ 'f G ~
''

.

f

~

H ;.,..,._ G-->
~

~~

N~ (~) ~ N<T(tl)

If

t,.q.2

H,

-for

~":1 .s~ ~ s. . d. IW: H5:.<f?.~:P:.

~ frn..~ ;-s~J

o-cl H1.

~ 14 s.~ ;~ r-s~ 1'

1-

G- ~ l~

h.. G-.
H,t ~ p

G-

fi,H~ it ftthl~



fw- s-...}~6-

.

.

H~
"~ ~ ::t L~ '·'t-1 . . If (H, II~ }t ~F.»)
w ~ - Hi. <!= 1_, 2.) ~ca. H~ /'"" G. So lH,ft~.J~=If,H;~_.
H!-:::.

N,t;.. IU H1 o.-.J
It;_

1-

!

Cl.t4L

I

S. H, H~ ;~ G-.
. It ~ ~ , .. ¥-2. IL.l: ·'f ~ it. tt....J .fi- s~ c+ G , lkrtr. ;..
~ ~ ~~s~::::l~
o.. "~ ~ ~ ;~ s~ of G /.euJ; ·
..;_ CX •
If 1t.;, i.. H ~ I~ H < I< ~ ~ ~{.;.. lid I< ~ .. ~ jrt.,."'~ :,_G-.
f3'j.. ~· "-' .> H ~ A ~l .
7L., fnrA~ s~ 1 G- ~~..:..J ..;_
u
J E 116-usn
·

.

A..

/'~

.

~t.v., ;-~ 1

..

eJ-

@-

fH-. ._

~ 1?: P~G- (P) .

;. "A..t , s.J,/.JJA_;.,. -1 1/::... 1.~ "1- JL .r4.f~ ?-? .:..
J~ .
FH" ~ f/1 _, H:L ..:. d'.. «ll:tnr.sl.. H, Ita. 1: I> ~ {,. ¥2 , . ~.
~ H,I'\H~ Jo.eo ~ ' ~ I:J P, '!· H,AH2.. ~ u..o~ ~
~ H1 " H2. ""cl ~ .t,.,.Jkr I1A. [II, H;). /Y q~l... , 'f G-,;
11:.. vd-~ ~ c..) t 2 ~ tk,.. 1' i4 . l.tlt ~c: ~ . 7k. ~~J
1- ~ 'r ,:.. G- <.N!. All.. f~ ~ Jut- '~ ~ ~ S~; - '/- owkc ~
~ ,~ . s" F C4M~t;, k
~ E «Uf _, i ~ tk ~ -~~
~

13.J:

":=t

1

~1r~r.

/C~Pj
r-

{,.L,-3

Fur
.-- o-J. k ~

a.

w2 ~

·

_

If K ~ <r > ft... t.t~ JJ!.w ..r~ "' J< ~ ;~~;,.G-.
Jj G&w r-J~ :1 or G- c.4-~ ~ ~ ; ~ 1'-s~~ :
P ("\ K. • .

I
I

_
___.;

I

T/..&;u. p~~ J~ 'J G- ~ ~ /k, ~ ? '"'I< ...,..;JJ.. K<J G
fn- . d. ~ .sJU!Le-L ~ 1- tf'. LLJ.Jc.c. o:'~ ~ u, Js" ~ r~
1 I~ ~ 'U elL t~ f. 1 . FN" ~ k, ~ 1<~ ~ )\.~ ..:.t>,
So ~ K, I') 1<.:.2.
--.J
PI"'\ (1< 1 r.l<z.) = (fn 1<,) r. (fn I<:L) . . F... r-tb.r >
Pn 1< 1 1<.2. =(f"'I< 1 )(Pr.K~).

r

7k ~~ .r~ 1-

(C)
~G.~

~

~

.5~~ 1U

X.
I~

s/l,f 1
~

~

alJtJ

L~ (~~·"~-~J

t~~'J-~ rnu.J-4~ -r-e;~JJ~

&..

-, H -::; ~

G

,;,

~J

~

'1 e-.

~reo~ +f"l7.~'J-~

~I H -=

.ltJ

,;...v-~~ ~ · YN-=

Y
l-et

') 7 -==

~1c~~

~ jx.,.,...j.,f~ 7- "- let
H Lc. o.. .s4j~ ~ G- -."J k.t:- N-= Nrr (H). l* Y ~
,JL y ~ X .A...:.J. 41-(. ~"'~r\ ....r:t ,..,.J..,..r H.
I/ 1 e- Y ...J t f;N,

U

we.

G-

(1..

~.:1

r;

{rr .ro...e. ?

'HI

-= :J t

'!Is € y .

~ N

~c..

/~ :J a..)~ · ~ ~

Y> ~ ~

C ~~~ X -1,-,A."";J~. S.,;c.c.. H::::~nS'l-,
H pht t;., £ a:o ~j~J;, !% 11 1 ~ {_ HJ 11'1

H'J ~ ~1 -= S~ • If
,__; ~~ o.lo ~ S~ . S, H *I 1 -=- H fan .t'"'-L 1 E- S~ . So 7:t e N "-J
y 1J = ~. 7Lv.. N r-e.~~ Y 1-~~~ ~r H ~ ~~~:. (T_
~~~ ~ ~v.rr():¢ 1u ..- ~ t,..JlA;~-~ ry-~t.J-Ju.. 1-- G-, "'
~~ Tn..-·J-~ ILL s~ ~- :...v-~ b:~ H. L~ .f e r;. tA-1 Lf
J-==- { H ") f(IJ.
JL,. 7 If -=- :r ~J J" Hi-= 7 ur r :f'H = :JS-1 • fl<..cc., ~
tk -~-~~ ~~c.JtJ~ "j 1 G-, H ~ ~d 1t... ~ T~-i7f-.'
~ I.:Jt~~ , T-= 7!-? for s~ 7 ~ N . 71.-t... '!~'} E 7 ~J +,..._'VJ~
J-(1 t-is H 1 -=- H . lli ;. r~
JL ~ ~ G . ~a. H
G-,
~ ~ ~ l~ 14 ~t ~~ '1
~ 6·' ~ lei.- H le. -.. s~ 1 G- ."l IJ. N-.. 1/G-(H).
~ u, H ;~ G- ·t 4-l ~
J ~
~ _t~if~ wrt"G/Ul.~Jt.t~-.- -r r; •

c.x. l...ve.

r

rrA

·r

~~ tr••:J-~ lb.. t~ f.tl- ~v...~ LJ H .
~~· > N rJ,"' G if ,_) ~
~ <..,..":} f,._;.J-~ w.r~ .J-J~ "~- (;..,
~ J ~{- ~· T I~
~.
I

"8 N
/

H

l

Y.

L, fk .cf~ur ef :1 ,;. G.
~ G-

. ~

·r

J

.to--U .;,. ""..

I

v

l.J: 11 a.L" G- ~) l,1: (;. r.~ X l-nr..r\4~ . 7h... ~ (j)
N ~ t,._._;J-~ 14 kt y 1 ~~_..);, '1 X ~J.. ~~ 4t- .:...v-An.~..i
&:1 H . B-t H -= N . l'k-u. I YI ~ I .

To 'T'CTVC.

/'

Lii)

I

~~.el:J > f IY/ ~ I for ~~ 1-~J-~ Wj>~J~ 1 6- tk....
H pN.. G Lq- U> .
If we. {;.Jec.. tk. ~~J-4~ ~ G k lc.. {""H ~ 1/:i.,..
1y I -.:: IN : H} b~ S·3 ~J ~ /'1-::: .! ~ tk.o~ ~ G-. 11<-C<. fl -vt~ c;,,
'
)I

-ecrJ·L...l:

t

B:J 1r ·6 , e~ 1-,.__J-.rl, '"1~J~
G- ~
IE -~""~< ~
.r~ r~ I< oJ G- . /" ~ , H ~'* IL. c~ I<J ~4~ if
Q..~J ~ .cf H ~ l<.:r . ~ /YI--. 0 · ~ H ~ c.qy.f4~ ~ ShAlL ·
~~~

~ ~ I~ 'Hht~ IlL c.rd~tr.&... for~~
.s~ ~ I~ ~ fw.o ~: . .
·
.

1- K..

~ (.t,,

L~

H J.-'! ~ .r~ -1- 6--.

~" ·/k ~

~~~ ~ ~-.L.l- .
U> H t...L)' c; .
(!i)

s ~ I<

.r4ry

F,- o-.:J

I< "/ G-

A ...

J

1\"'j

J "G

J

H ~ I<" 1<.~ -:.y~

.

E\le."'J .t~ 1 ·G- cJ~ H -4 ~71~ ~ G, ~... J H ~ ·
,..~, ~~ '"' ft4 ~~,q_ '1- Al4AJ . +~ J.:.t-~<-f ~Jo..k $~~ 1
{jliJ

G- .

.

We_ ~

/..~ b·l.
If

-to . L4
(.i)

~

If H ;~ 6

a ... J I< <r G- .,

~.. HI< i"'- G-.

I< <1. G- ~ I< ~ ff.) ~ H />"" G if J ~ ·'/- H/1< fu"' G/1<.
~ G ., .· H ,,.,, HI< • .; HI< J>m r"t , Ltc. li-p~ G -:(Jl..

fi-~i-~H-"7·~ ~

-S.;,.. . HI<~

>

ttl&

io

Art

f•eoe (iiJ

.la-...c

»

fU:

St

~

otd T

{liJ

H9-

,r , ~~~J r~:

~--IU- ~~

.•'•

I

I

!!;-.

W-e tt.o-IL M...J- .r~ ~:J ~ 1 {,.{,.

[p)
~

Lt.~ b. b 1

7l.. ?t.~?A.r$ .

;~~ s~""ts

1

cue a.J,"...._j.. .

I~ l'~.Ai~ ~ -~ 1- S:J~ S~J ~ ,J.~ .
Le~ . 6.
~:1 .s~ ~ .;. ·~ ~ -J,~ Jv.bs,....,. ~ ~"~
L~---.. {,.{, 3
L~ H }>ht. G- . a...J {U: N = NG (H).
If f~ d.__._,J. 1- /tA.

'2.

~J-re

"J H ctze ~"j~ ~ (;. > ~ Ate. ~"':f.k ,;.. N. If f~ A~
..J'~.s 1 H ~re.. ~J'-':J,.h_ ~ G- , ~ cu~. ~"JJ;, ,;. N •'
t..~ ~- {,Jt.
i..d H ~ G.
~ . "-o ~ J..:.f...:.el:: . ~ of lk
u,J~

~ ~ ~ '!/J:i_ ~ G- ;

'} H

o-J ~ H

LJ;

b · 6s

~ "'"~ c~

. [s
~

~ L

£...,)

1

H h.. G.

'}So

;n-. G

H

W:

N

= Nv (fl)

""'cl

f.i

F~ ..

7L,.. KN ·= · G-.

LJ: L-=

'-o -<f

L1

~ L-f"-2..

!<.
)

....J

'

Br 6 · 3. (!i"iJ
.s~

6-J H

u- .

So
>

~

a-;

-t

/3' '· ~s-,

~ ~ . -~

l~--.

{, · ~ b

--.c\

Itt,

.

.

.r~ H 1 G- _,
G- · cvL_ci,

<1

~c.c.c.. H ~

·

s~ .r~

~ G-.

t H I<}

-=

L..,._,

S~u. H ~

Lr= G-.

<1 • ·• 4

1.,

_.

I



-=- { H c;. ~ k

J<:.

if

H~L&sln..G-.

LN-= G.

~UL H p~ c,. ;, ~Joe ~ 1<

~

J.wf-~cl- 7t~ ..r~r

~~ oj . '· l,s . i..ct k E- G- . . 71...~ 7- {H., H}} ~ I<
./o-Q, 7 €; I< • . 1-k.CL. l = (t?) ,-, E: NK = I<N) .. ~ ;II

~


~

Ao

~ k . ~"'J~ ~ G-.

L~ n.-.r;._

/t:.e..,. /<

Ck..4l

"'--J

~o

I<N =G-.

G- J ~ ~ I<~L.-_1

'--r-,. -a

u

·

~

....~

kfi,.__~

~.u- H _; /AM .;, 14 .r~ ~

s~ ~ 7 "'"- ~~ ..r~·

1l~ ~cu-G



A . ;~ s~

tlb ~~~ (~ 1M." ;1;,-dJ-).
F&r ~1: H trn. G- 'ka H)4 H

C4Jl"-~ k.
.

,

p.u...-t..JI...
.

~ € G- . ~"" ~ ~ ~

...;,1i. w.1
-

r ~ 7-:

'1
.

{H ~ Hi].

/?>....t HH'J=HsH _w-Ll .::.Y,~ T--HIIt JIJ :t·'"f, ~,._Ytj b; 1·6V.iJ,sat-r;t!
le~ &·br
lei: H r~ G ~ l..t H ~ K ~ N-=Nr;.(H) .. 7/..e"' 1/&(K) ~ N

I

~

r---

__.

I< r~ G--

S'i'lf!;U..

if

~,)

~

J</-=-· K

,

.'/

yf



L ,._, ~'~

. -

~

H1' .-- H

KfH
G-.

~ NfH •

S.Ac:c.

~j~a.t: k H •.:.. :T- { H, H}J ~

I<~ N,

i. w4"o..;.J

·

J..~ Ht-::t K. • BJ: H'~.:,
~ k. J.k.c.e.. H 1- H -.a t ~ N.

we.

i

It K ;,-... G ~

;h\.

k.fH

{ H> H '1J

w

N/ H

:r=-

$

!

c,...j~olL

..:. 7.

.so l<fH ;~ ti/H..

if

~~ ~

fL.~ ;,., A~t .d...-"....1: j ..;..

E: (;.

H1I = II ~ ..r.:-.c.. H t'"'- G . 7L.... H<1 I< '{s
J>""- N, c.Je lv..vc.. k' '!J-I< fer r~ '! £ :r;-(K~J<'Ij

{ K .J I< 'I}

tt..1:

sf4.J..

4J ~CA-

~ ~ ~ JJ. '} ~

fY

n-

e J.

K ~ K'l

Ate.

G- ~d .so I< prn CY.

W: H/k 'At. ~ f-J1h-..q,.. .l r-s~
~ "'"':1 J'J~ ;-s~ 7 t1 H ~ · f'~'DtA.~ ~ t;_
S~c.t... Hjl<. ~ ~ ;-~ ~ ~ ~ H-=- KP. L.d-1" '-· ~~

L~---.. t,.t~
G-/K.
J>~ ~

lei: 7-=

a..a

F,- ~.:J '

S~u.. K
~"d So :Jj ~ T

J

E-

'·.2.

I~ J<. ;,.. N.

;I

K'lk ~ N.

.to

13~ ~

Jof

It,..._ K.. tn' N l:1

Lu- ·" <J

{P> . p!j. , 7kn

c.

Aoo.J

{f/) Hr} = ' TJ<

~ s.:..o.. H p~ 6-,

t...e

lv..vc,

.r~ 1 (:- :r~ r (: x . 7/vz... P ~ ~ pt '1
s:J lt,w
} - S~n -J- H-= Hl7
~ ~CL ~ 4t-e ~~,J;, ~ !L_.;,.. -~
7; ~ { F > pt ?} . B.....t J, -s;. :r ~ ? ~ :r. ll-e..u.. P ~ ?'~ ctH. ~lcf.l;_ ~ 7.
7l~ "-A ,fw- .JL 1 ~ G- ..~ ..ro :P r (;..
7/..io !..-.-..._ .s~ /U ~ve~ ~ r-3~,. "f 6/K ;. /L-

for

H :r? 1 = H

4#-e.

~ /ttL ~ t!f~

k-..Je.

; -s~

1-

- ' Lfl.~ '. /,'

=i

4(1-

G- ~ (;-/K

of .r~ />~

C.

L~ G-

=LM

~H!, M ;;

o-

k~

t-tJtr111Af -t G

-.-d

Ld ? l«- "' S:1~ ;-.s~ "/ L;, · :P,:::. [M> E] ~
H;· PP, . 7k.... H .:- f~ ~ (Y.
Pn>oJ : LV-= PM 0
J;~ ;-s~ 1 & , &k N-= NLCJ') .• ~CA..

L n 1'1

.

6..

G-

w

=- NM .

G-JM

k,.._v«. 14 .f#li~ ""~ 4

Lc.t Hi~ 61. • 1L.- Ol~ =

~~ j-.s~s ,

P}M

s~

1-1

<t

~ N<i-(~)
Cr ~ .." fi ~ lJl ~ P1
nM=-.J.
We.

"=

~CJL. ~ ~ = 6l ~J s = 7J - a.dl 7 E: N ~ j t: M . 8 ~ 'P P o.J .ro _
f,'J = f,
~ l.e,.CL H. = H. 7k- H 1 =- HJ. IJ.J; P, <1M bd- r~f(!,"J
'
~
.
~
a-J P ~ P [P;,11] -= H • J..k,.u., H = fl , . ~ So £ll ccr4~ ~ <rnL
~"";! _J;_ "f If ~ .G-- • So II tr. c; A.o sf,_/; J ~
/

J

(E) . ~.... ~-8
7l..c.
til G io ~~J.

~ C~-A8J-chJ .,... ~ ~ G- «~ ~~

(!i)

No /'~ s4s~ 'I lT

Ju...~

(jii)

E~~ .r~

Civ>

E-w~.~ ~ ..t~ . "1 6- ;.. ,..~ ..;. G.

k,

~ sJx~ ~

1 ,G- .

tV)

Ew..'V'j . 1n-4X.~ .1~

(.1"0

E~":: SJ~ .s~

1- G- ;,

7

..: G--.

£t.

')\.~ ~ f7~. ~~a"- G'.

;. . -~

&

~ tY.

f~ r (j) ~ (fi) · F~ lJ: fl k "'- /'~ ~~ oJ
i. -::: G-0 < G, < · ~ . < Gr : G- Jc. o... c.e.J;...d .se.~ ~ G- .

-(U.st

~

~CA..

~ ·Fl~ _ eoJtU.- H

.J!id..

>

-=

G,_, '1 ~ ,-,

17,_,

~ ~

U G-c: k lt:c,.
l.k .f 6 H a.J 7 ~ &-, •
~-' s7 -= ~-1 7 s·

1 G-jc;.,_, >we. A~
H > ~u. G,_, -$ 1-J b:J J+:..ild,_

itt ;,..... lk.. c.a.,.:::-,c

G, jt;-._._,

.S,;,..ce..

~~,.w

.:... li..:-

(7

s~

-j i..

T~ 'J '! 7-' '" H . ~ ~ fw- alL ~ ~ H ~ 7 € ~-. I~
G-t. ~ NG (H) .
~Cil. G-i $ H 7 ~ ~c.l.Jq IU H io ~ Jw~ ~ G-.
{ji) =7> (j;i)
(jli)

:~,

=7

;..

~ ~
Ffrr /,3 /,. =t >

(j>/)

(jt1) "9 (Y).

~~ cJ:,"-~
ii ) ~ (_v)

;_.

~

>

ltc,

~

'·'·
A.

~. ~ s~

~ "J:

i.o

b;; ~.(,, _ ,_; 6·62.._

t>-

/L,. ..te.c.,...J

V.

'"'""'~ •

~c-- ~~

~~ ~

ck-.r .

(v) ~ (ri).

Cq.,.j-~

~.

Far

1-

x~?..c.r

a-J ~ ?t~ "~·

"'-A'j.,;_J, .t~

~ )l-"'-~~ S~~ s~

Al~J~

,.

(!~) ~ Lvi)

.fM,..CL

wl:.cJ.

~ ul,~

SJ~ .r~~

~p~ -

I

LVi} =7 (_i) ,

~ ~~

(M.

I G-/ .

fJ.z_ )t..Cc.cl lt.c, ~ ~,

L~~ 6 •1 .

LJ;'_ H ....q G ~ ~ <1 G- .A--.l H 1"\ K-=- 1.. ?L,"'
~""~ ~ ? H t:.()-.,•••, .. wli.. ~ ~t;i · ~h-~ -f I< •
. Fvr lJ: ! -E H > ' ( I< - ~c~ _ j = ~
_,!'I. 7k" s-~-'s E I<
w So ~ K > wt4 I '1 € H ~J s .•w~::~~f H. k..a.. H r\ K =.f. ..

r

~ ~ .r~ t.

,-I

...; s?=?f·

'~· .~

;


.· ~"·\,

I

·'
'
'l
- - -- -· - - - - · - - - - - - - - -· --1
'

s.._,,~

?WW

k.t S ~ ~ SJ~ ;-.r~ ~ G- ., S-:F 1
~;- 1. s.2.. (!iJ.
L.d T /,e, "'" ~w 'l-~

Jt.AC G =F t

a-41

w z-=- :rs . 7J..e.,., z-=;. t
1 G- w:1J. t-=/= /> · ~ Z" T-= 1.
~

-::t G--.

~o £

<1

6--

'J Lr •z . ~ T ~~~ Z ~;r 6 •7 .
~o S ~rJ.la(;tt Z = } S.
7L- C = CG- (2:) ~ tl.. ~~ '/..~

Z eLv S

oJ

ftw

G-

:>

~o

8:; ~~~r.:. T

z

<: G-

z ~ ~ t=-P.

,JL ;~

!30

s. 1:, > z T ;z ;..

T

G- ,

-<J

Wt'.

~ ZT

S:J~ s.~s

"-:1!~ ,; ~

1
G-/z

I:~t,_,

4

G/Z

~

-=t

G-

AKJ

a-

lt.

~ra.l .r~

1- G-.

b:J

a..J

z~ } G- .

s.;z . ·s~

1

ZTjZ.

Jo

~ tdL ~~~ ,

<:1

S·lf-(/iJ.

z

4

/3J lit.. .:..~d-~

<r,;z

~

S~'«- Z ~ }G-.) 1=G-o <Z=G;·<··<:G;.= G-

7".~ t;.. ~ ...

"+dk..t.

---------------

--.

r;. a-J

~ Ik-e.,_ ft..

G-/Z .

c.&,J-,..J., ~ WrA ~

Z=C-, < G-.z. < --- < G-r-= G-.

u

z- s~

So c-= G-

-----···-- --· --- ·-----------

-

'

-- -

------ ------- - -- - -- - - - - - - - , - - - - - - -- --

- --1

Citation

Hall, Philip, 1904-1982 , “Philip Hall Lecture Notes on Group Theory – Part VI ,” WUSTL Digital Gateway Image Collections & Exhibitions, accessed April 20, 2024, http://omeka.wustl.edu/omeka/items/show/10788.

Document Viewer