the t~omf{;o~ g-roups. - school of mathematicstl/calgary/thompson.pdf · ,. ~~omr:()n ~ g-rcup f ~:...

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-" THE T~OMf{;O~ G-RoUPS. TOM LeiV\sber & Mo.rcelo ~d"fE!.. Ma.~. GRI 05086', s~ b~ f\}\.t~elJftsu~ 0

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Page 1: THE T~OMf{;O~ G-RoUPS. - School of Mathematicstl/calgary/thompson.pdf · ,. ~~OMR:()N ~ G-RcuP F ~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O ~6~,~ (i,) f is piec~w ige.. [iYl€Q.r

-"

THE T~OMf{;O~ G-RoUPS.

TOM LeiV\sber & Mo.rcelo ~d"fE!..

Ma.~. GRI 05086',

s~ b~ f\}\.t~elJftsu~0

Page 2: THE T~OMf{;O~ G-RoUPS. - School of Mathematicstl/calgary/thompson.pdf · ,. ~~OMR:()N ~ G-RcuP F ~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O ~6~,~ (i,) f is piec~w ige.. [iYl€Q.r

ThVV\

C(j((/\ e£) Cl-

--rh eCA\Atorv\6'(p ~ is'''' ~~ £- t1A.e

.IJeNlrot~t- o~ed- IsI L-..I

§2. §s

nd"\MfScM -5 jrvvvp F .I

§J

Page 3: THE T~OMf{;O~ G-RoUPS. - School of Mathematicstl/calgary/thompson.pdf · ,. ~~OMR:()N ~ G-RcuP F ~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O ~6~,~ (i,) f is piec~w ige.. [iYl€Q.r

--

,. ~~OMR:()N ~ G-RcuP F

~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O

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(w.) eoc.r-~ c:k ~oW::s ~ eo&! piece

o.re d~~,- raJ:i~ls .

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EF

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Page 4: THE T~OMf{;O~ G-RoUPS. - School of Mathematicstl/calgary/thompson.pdf · ,. ~~OMR:()N ~ G-RcuP F ~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O ~6~,~ (i,) f is piec~w ige.. [iYl€Q.r

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Page 5: THE T~OMf{;O~ G-RoUPS. - School of Mathematicstl/calgary/thompson.pdf · ,. ~~OMR:()N ~ G-RcuP F ~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O ~6~,~ (i,) f is piec~w ige.. [iYl€Q.r

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is (Ani&e oa!;n~)

( 1" ~ is ~lk.J ~" C«t -= :s&ict ~ Q:;d..)

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Page 6: THE T~OMf{;O~ G-RoUPS. - School of Mathematicstl/calgary/thompson.pdf · ,. ~~OMR:()N ~ G-RcuP F ~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O ~6~,~ (i,) f is piec~w ige.. [iYl€Q.r

ne ~er..c ideMp>f.ent-ob~ (CO'Y1t-illtted)

An id2.rnpo~t- °k:uec.t in ex fflon Cov-c-'m, is 0-

f'4-ir [MJf ) where ME 1IL ~t"IJ.. r: M$ M ...=.., M.

Q . W~t- is i-he +ree MOn CA#: o-r. N) ;cJ.eM~fe/t-t:-

o~eck?

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iklV\~tent- obj~.

cA=(IA(l Ae2.L> L "'

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(If' ~ lJ" ~ "';id ~ -, "" , ,.",; . . ( .. . . . ...' ..

E..~.

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A. 1-+F ( w~ere + is corrnA.u.c.t In G:k)

This C\nswer is ~ u.i"oJ~~t ~:

ThM; A~t (,A) ~ F .

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Page 7: THE T~OMf{;O~ G-RoUPS. - School of Mathematicstl/calgary/thompson.pdf · ,. ~~OMR:()N ~ G-RcuP F ~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O ~6~,~ (i,) f is piec~w ige.. [iYl€Q.r

'3. TH£ f'R.a:J t::

Cona-et.e ~: ~tU2. A b~

ob cJ-::: N J

ACM,t\) '" {bijed:\cMs [oJt'tiJ ~I.oJ~ so6s%~ (j)-(;.i.i}1

M~ Vl/r'.~ W\\,,~ ~ J;.~.

A r~:

c

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r~l~r '

MOt' ~ JiJ<

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{, ;1: n:::1

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. UJ\i'letSQ.L p~~ oC ~ iMMedACA.~ ~~~Oi"~

. e~\Ac.;f-- tle5ifirCJV1 &. ~o~c.ness <3i~

cA~ l+r.

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Page 8: THE T~OMf{;O~ G-RoUPS. - School of Mathematicstl/calgary/thompson.pdf · ,. ~~OMR:()N ~ G-RcuP F ~: F is the ~/'b).tp ~ bijediChtS (O"IJ-£ro"O ~6~,~ (i,) f is piec~w ige.. [iYl€Q.r

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A c.onJ~-icl€M~ on ex ~~ G- is

0.. F-jr (O~ 3l W~ 0: G- ::> (;. anJ.

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~e-(; ~ V~J y(r(~))::: 5' o{':X).~\.

ThM: Let- Cr;.J013) be. &he io,tfo1 B~

w;t1A 0\. ~~- rJetvlfo~, ~ Q;::.1=-.

Q. R.eloBOVI~ ~€. ~ -n,~~ '?~

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