# math 111 Final(fall 2010) by adnanbasar

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```									                                                  MATJ-4 111
FlNAL EXAM

dj        D~~inc... (:( posi+;y~ re41                             I1U1ttb~.

2).) Le,t G h~ ~ "roiip aiiq iiC G CL .s()~~up.                                                                  J)e./il'tG
Ha. == [X6 GL x=h« -for ~o,.e- hE.l-ll ~ SD"'~                                                                  a~6.
Similar'l               oI~/i,,~          a-H   o     00    IAJ<'    alwQJs have                a.U    ==   Ha.        ?
tV      k:.t G b~                       finitc, jroup-            Sur~~               LGI=-        -2-11-11.     Si"OIc1        :
a.U      ==   Ha.

3) oc)          Skow -1iitat                    -#i~ I'I"Mber of.               eVeA alk:l      ",Jd per,""Tat,t:M~ ~
~UAlo

b)    Sh()I,cJ        fl.,,,,t

4)    1.1.)     Let G b~ et                       ~illik:. jN1"'P,               Si,OIU      -#fat.   orJ(Q.) Jivid~                       161
-Por~ a.~G.
f»       Snoid ~                     4
1&1
::r   e,..)      «e G .
c:)      Shotcl      o.        a." == a. Mocip                1t'r anJ a e J!:.J                     p:.et      pr',.,e,.    o

(Ui"t:             ..fI1ittk       of!.      (~t)·)                afld       b»)
5) F{nJ                   ~c.d (420.1 ~ 5S)                              tJ::Ji'J:j       Euc/ici         a{,orifl,,,,.

b)        :Sl1oiIJ        -+kat            (o     d~            not .fador                c.1I1;c:rt(e~     iiito pr;"'~~
in        .:e3:.    CVAO        J
e~                1"~:st;,,11 .::) .,orih                 40    roint~.
Try       +~      M-sy .~~              .jir:st".

```
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