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Groupes
The document appears to contain a dense and complex arrangement of symbols and characters, seemingly lacking a coherent narrative or specific content topics. It includes references to terms like 'touscours.net' and various mathematical notations, but overall lacks clear, understandable language. Thus, it is challenging to extract meaningful information from the text.
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- 1. ∗ !" !"! ∗ ! # ∗ $ % & ' ! ∗ ( ) * ! ! ' # ∗( " +,+! =∗=∗∈∃∈∀ =∗=∗∈∀ ∗∗=∗∗∈∀ ) % - # . ∗ ' ! ! /, $ ( . ! ∗ $ ! # ∗ ( 0 12 +• " ( +• ( ו " ( ו " 3 × ( • , { }= 4 ♥ ! ! ' ! ♥ 5 6 =♥=♥ - ! 1 7 8 9 . !" ∗ ( • & ' ! 4"2 ! /, ! ! !" ( . # : ! 2 ( ::=∗= : ; ! 2 6 ! ! ∗ ( touscours.net
- 2. % • * !! ' # ∗ 4"2 / ! ! !" ( . # ::: ! 2 ' # ! ( :::::::::::: =∗=∗∗=∗∗=∗= 6 ! ' # ! ( • =∈ =∗=∗ ' # ! ( • ∗=∗∈ =∗=∗∗=∗∗∗=∗∗∗=∗∗∗ <=<=<= 1 =∗=∗∗=∗∗∗=∗∗∗=∗∗∗ <=<=<= ∗=∗ • - # 6 ∗∗=∗∗∈ ( 6 ! > ∗∗ • 7 - !"# 9 ∈ ∗=⇔=∗ ∗=⇔=∗ % ! . =∗ ∗=∗∗ ( 6 =∗=∗∗=∗∗ ( ∗= . ∗= =∗=∗∗=∗∗=∗ 4 ! ? % @ • - ∈ =∗=∗ =∗=∗ % 4 $ $! ! . ∗=∗ ∗∗=∗∗ . ∗∗=∗∗ ! ∗=∗ : +,+! = 4 ! ? % ( # ! ! ' !" ∗ $ / ! 2 ? ! ? . =∗ =∗=∗ %% %% ∗=∗∗=∗ %% A == ( • & !" . ∈ ( 6 ! %B=∗ )B=∗∗=∗∗ 6 ! ∈ B ∗=+∈∀− =− BB CB touscours.net
- 3. ) , !" #∈ BBB ∗=+ BBB ×= • & 7 ! 9 . ∈ ∈ ( 6 BB =− BB =− 4 ! , ( % 1 7 $ 9 × $ $ + 4 + 4 ' # ! ∈ − $ ! ( + 4" ( + 4 ' × $ × ( 4 ! ! × + −−− + − − −−− −− = =∈∀ ==∈∀ =∈∀ = =• == ==• =⇔= =⇔=• =• =• C ) 1 7 !! $ 9 $ 2 + $ $ + 4 C " ! + 4 ' # ! ∈ − ! ( + 4" ( ( + 6 ! # + : +,+! +=+∈∀ 4 ! =−−• touscours.net
- 4. D −+−=−+−=+−• −+=⇔=+=+• ; −+− +=+∈∀ = =• =+=+• (( ( C(C ((( −=−=−∈∀ (− (( ((( ×= +=+∈∀ 2 ! + - ! 333 ×××++++ + ! . $! # # ( 6 " ! ! / ! ! ( ! ! ! ( ! # ( + 6 ! 2 / ! ! / ! ! ( + 4 $ =∈∀ ! / + E &! ∈ + * ∈ ' # , $ − ( ( F # ! ! " . ! ! ( . → ! { } { } =∈∀ = = =∈∀ = = 55 ! # ! ! ! $ !" $ + ? $ $ ( 1 ≠ === === touscours.net
- 5. G 12 + 6 #{ }((()%= ( ! ! H( • * ! ' ! % { }τ&!% = I { } { }%%&! → { } { }%% →τ ! %;% == ττ * ! &! &!&! &!5 ττ τ τ • * ! ' ! ) { }:&! ))%%) τττ= I { } { })%)%&! → { } { })%)% →τ ! === ;; τττ ( { } { })%)% → ! );)%;% === { } { })%)%: → ! %):;%:;): === ( * ! &!:: &!: &!: :&! :&! :&!&! :&!5 )%)% %)%) %))%)% )%%)) ))%%% )%)% )%)% τττ τττ ττττ ττττ ττττ τττ τττ + ⊗ I # # × $ ⊗ ! ∗ →⊗∈∀ 1 !"# $ ! ( . %≥∈ ( 6 ! ≡ ∈−⇔≡∈ " ! ! ( 6 J !≡ <=≡ touscours.net
- 6. !"# $ ≡∈∀ #∈=− C % ∈ ≡ ∈− ! ∈− ≡ ) . ∈ ( . ≡ ≡ − " =− I ∈ − " :=− I ∈: ( ∈+=−+−=− : ( ≡ ( ≡ 2 $ ' # % ' # ) " ! !"# $ ( $ K ∈:: . :: ≡≡ ∈− : ∈− : ! ∈−+− :: ∈+−+ :: : + ,+! ::+≡+ ( ∈ !"# $ ! " ! ! , ! ( " ! # # " $ ! ( 6 "# $ <=≡⇔=∈∀ ( 1 . ∈ . = ( /, ∈ ≡ 2 $ " , ! ∈ ! <=≡ ( . <=≡ ( . ∈ ( <=≡ ( <=≡ ≡ $ ( ∈ ( ⊂ ( ? ⊂ ( = ( "I "# $ ∈ ( 6 A " ! !"# $ ! ( { }∈=A ( ! A ! ! ( ∈ +=⊕ ( ⊕ ! ! A A ⊕ ( • . ∈ ( 2 [ ]C −∈ # = : +,+! # <=≡ ( 1 1 −= I [ ]= +<≤ ! +<≤ <−≤C : +,+! C −≤≤ !"I "2 ( [ ] =−∈∃∈∀ C touscours.net
- 7. L A , $[ ]C −∈ ( 6 ! ! # ! ( . [ ]C −∈ # = : +,+! # <=≡ ( & 2 ! ∈ # =− ( += ( 6 C −≤≤ ( +<−+≤≤ +<≤ [ ]= ( 6 C −≤≤ ( C <−≤≤ [ ] C== ( =+= ( [ ] ==−∈∀ C . [ ] ≠≠−∈∀ C ( A , $ [ ]C −∈ A ! ! ( • F ! /, # ⊕ ! : +,+! # ∈ + ! ! # ! + ! ! . : # =: : # =: ≡: ≡: +≡+ :: ! ::+=+ ( /, ⊕ $! ! A ⊕ $ ∈ ⊕⊕=+⊕=++=++=⊕+=⊕⊕ ∈ ⊕=+==+=⊕ CCCC A ! ⊕ , $ C ( . ∈ −= ∈ ( 6 ⊕=+=+−==−+=+=⊕ C ! A ! ' # ⊕ ( 1 ⊕ $ ∈ ⊕=+=+=⊕ A ⊕ ( J K ⊕ . × ( . ! ( 6 ! # + ! × # ∈ % × ∈×∈∀ ) , " $ ∈∈∀ − touscours.net
- 8. M . + !× × ! × ( + /, × ! !" % + 4" $ " ! ( + E " # ! !" + 12 !" $ ! !" ) ( 0 12 + 3 + ! 3 × 3 ! 3 × ! 3 × { }∈% { }− 3 + ! + ! 3 × + ! 3 × { }=∈= + ! × { }=∈= + + ! + { } { }<=3C πα=∈∪ 4 ! ! ! 2 + ∈ + ! ( + . × { } ! + ! + + ! + { }:&! + ! { }:&! ))%%) τττ= # " ( . 3∈ ! { }(((% $! ( . { }⊂∈= σσ : +,+! # " ! # # ∈σ σ / $ σ ? ! # ! =⇔⊂ σσ + ! + ∈&! + ⊂σ ⊂:σ ⊂:σσ + ' # ⊂σ ⊂− σ 1 . # ⊂σ ( =σ . ∈ ( σ∈ ( & 2 ! ! # σ= $ ∈ =− σ ! ∈− σ "I " ⊂− σ ? " # − σ / $ + + ! + • 4" ! ' • { }∈λλ I 2 ! ( • { }CC =∈ • I ∈ I ∈ • 1 ! + ! # , 2 • 1 ! + 8 , 2 touscours.net
- 9. N • 1 ! •1 ! @ + . + ! A = { }{ } { }{ } + )CD%CGD)%CC ! A G ( % D ! { }D%C ( ) ! { })C ( 6 ! # !" ! % D !" ! ) ) !" ! %( 4 + ! + ( /, I ∈ ! + ! ( O + + !" P . + ! # { }C ( & ! ! " !" 2 ! 3 ( " 3∩ $! ! ( ! ! ! ≥ ( = ( 1 /, ! # ∈∈∀ , " $ ∈∈∀ ! ⊂ 4" . ∈ ( 4 ! $ ! ! ! += I ∈ [ ]C −∈ ( ∈ ∈ −+=−= ( ∈ ( ! 3∩ C= < ∈ + ! 2 I ∈ ( ! ! + . × ! ( + ! ∈∈∀ ∈ ⇔× − 4 $! ( " . # ∈∈∀ ∈ − touscours.net
- 10. C ! /, ∈@ 1 = ∈ ∈− ( ∈ ∈− ! ∈−− : +,+! ∈ 1 & ! + * . × ( ! + ! + ! ( . ∈ ! + ! ! 2 ( E ∈ = /, ∈ # ∈∈∀ ( . ∈ ( ∈ ∈ ∈ ! ∈− ( ∈− ( + ! × ( Q . + ! . × ( . ! ( 6 + ! + ! ( & ' # ! /, ( " ε ! + ! " $! ( ! ε∈ ( " + ! ! + ! ( 6 ε∈ = + ! { } ! + ! " ( 12 + A { }D%C% = { })C) = AG = ! # G ! A { } A)% = { })% ! A + + ππ %% = + { }:&! ))%%) τττ= { }:&!= ; { }:&!: = ; { }%% &! ττ = ; )=τ touscours.net
- 11. . × ( 6! # # " ! : +,+! # " 2 ∈ # = : +,+! =∈∃ - # { }∈= 1 + . + ! ( × , " $ $! # " { }∈ ( + 4" { }∈ $ + ! & C = ( & × # { }∈∈ " = " : = I ∈: { }∈∈== + :: & , " $ # { }∈∈ " = I ∈ { }∈∈== −−− ( " ! + ! # = ( { }∈ + ! # " ( - # " ! ! ! !" ! ( ! ' # # " ( 12 + + { }( =∈= !! $ * + ! { }=∈= ( + A + ' # ! # " + × ' # { } ωω =∈= I π% ( F ! 7 8 9 . R ♥ ! 2 ( ! R $ ♥ →ϕ # R ϕϕϕ ♥=∈∀ 12 2• ! + $ 3 × touscours.net
- 12. % • ! 3×+ $ 3 × $ 3 ×+ • ! + $ + θ θ• ! 3 + $ 3 × • 4" ! $ + ! + " ! + $ + ( 0 $ . ϕ !" × $ × ( ϕϕ ϕϕ ϕ ϕϕϕ =∈∀∈∀• =∈∀• =• =∈∀• −− • " ! ( • ϕϕϕϕ ×=×= ( 4" ϕ= ! $ ! =× ( =×= − • . ∈ ( === −− ϕϕϕϕ ? =− ϕϕ −− = ϕϕ • . ∈ ( F # ϕϕ =∈∀ C= CC ϕϕϕ === . ∈ # ϕϕ = ( ++ ==== ϕϕϕϕϕϕϕ 6 2 $ ! ( E ' !" . ϕ !" × $ × ( 4" ! ϕ ϕ& " ϕ : +,+! { }∈ϕ ϕ& + ! ( + ϕ& ϕ= + ϕ& × . ϕ&∈ ( " ϕ I ∈ " ϕ I ∈ ( ϕϕϕϕ &∈=×=× touscours.net
- 13. ) + ϕ& ," $ . ϕ&∈ ( " ϕ I ∈ ( 1 ϕϕϕ &∈== −−− . ϕ !" × $ × ( 4 ' ! ϕ ϕS ! { }S =∈= ϕϕ ϕS + ! ( + ϕS∈ =ϕ ( + ϕS∈ =×=×= ϕϕϕ ! ϕS∈ ( + ϕS∈ === −−− ϕϕ ! ϕS∈− ( * . ϕ !" × $ × ( ∈ ϕϕϕ S∈⇔= − % ϕ / $ { }S =⇔ ϕ 6 # $ ϕ ϕϕϕϕϕϕϕ S∈⇔ =⇔=⇔=⇔= − −−− % . ϕ / $ . ϕS∈ ( ϕϕ == ( ϕ / $ = ( { }S ⊂ϕ ϕS + ! ! ϕS∈ ! { } ϕS⊂ ( "I " ( - # # { }S =ϕ . ∈ ( . # ϕϕ = ( ϕS∈− ( =− ( = ( ϕ / $( 12 4" θθ ϕ 3→ ! + $ 3 × ! ' π% !" 4 # ! ! ! ! 2 ! ! ( touscours.net
- 14. D . R ♥∗( . →ϕ →ϕ ! 2 ( ϕϕ ! $ ! ∗ ! ♥ ( . ∈ ( 6 R ϕϕϕϕ ϕϕϕϕ ϕϕϕ ϕϕϕϕ ♥= ♥= = ∗=∗ 1 & ! . ϕ / ! × $ × ( − ϕ / ! × $ × ( 6 ! # ϕ ( 4 # " 2 ! 2 ! # ! 2 ( . ϕ / ! × $ × ( . ∈ ( . ∈ # == ϕϕ ( : +,+! −− == ϕϕ ( −−−−− ×=×==×=× ϕϕϕϕϕϕϕϕ − ϕ ! × $ × ( 12 =< %% ∗−• ππ + I∗ ! =< %% +=∗−∈∀ ππ : +,+! =< %% +=∗−∈∀ ππ =< %% ϕϕϕππ +=∗−∈∀ I =ϕ # / ! =< %% ππ − ! π% →• / ! + $ × / ( . ' /, " # ∈ %%% ===+ + πππ ( / $ # ∈ " π% I ∈ ( F " / $ ∈ # $ ∈⇔∈⇔∈⇔=⇔∈ ππ %S % ' ! ! " / $( π ϕ % A → I # = / ( touscours.net
- 15. G /, # !! ϕ : +,+! # π% ! ! # ! ! ( . ! 2 ∈: # := ∈− : ( S:∈− ( := !! $ ππ :%% = ( " A:∈ " $ = ::= I ∈: :: :%%:% ϕϕϕ πππ ===+ + ( ϕ / $ # ∈ " π% I ∈ ( ϕ / $ . ϕS∈ ( " I ∈ ( % == π ϕ ( ∈ ( C== ( { }CS ⊂ϕ ( ϕS + ! " ! " ( ϕ / $ ( ϕ / $( × A + ( - # 4 7 ? , 9 !"# $ " ! + 1 2 $ "! !" $ + 1 ' # , , + 1 $ ! ! 2 Q T + ! $ ! $ ( + ! $ / ! $ ( + ! ! ! $ ( + ! / ! $ + ? ( ! $ + ? ( ! / ! ( . × ( * ! . 3∈∈ ( $ # $ ! ! ( % & 2 3∈ # = ! ( ) 4" { }=∈ " ! , { }C " ? ( 4 # " ! ! $ ! # !" ! ! , ( touscours.net
- 16. ! →ϕ (ϕ ! + $ × ( 1 :: : =∈∀ + ( 6 { }=∈=& ϕ ϕS ! + ! ! ' I ∈ ( + . C= { }CS =ϕ ! ϕ / $ ( ϕ / ! =ϕ& ( ( + . ≥ { }C ((( − = ( 1 { }⊂−C ((( ! /, $! ( . ∈ ( " I ∈ ( 4 ! $ ! ! C≠ ! += $ [ ]C −∈ ( { }C S ((( − =∈ = + ∈=== ϕ !"I " " ( =! "2 ! ! ! [ ]C − # ! = 2 C −≤<≤ ! $ ! = ! =− # C −≤−< ! ! ! ∉− ( $ ! # % ) . ( ! ! = ( ! 3∈ # = = [ ] ≠−∈∀ # C = # [ ]C −∈ ! 1 !" " ! ∈ # = " ϕS % ) ( . ) 6 ! ≥= { }CS ≠ϕ + ! ! ! ( ? % ( 12 A + % !" ! ) { }D%C% = ! ! ) / C%%%%() =++= CD%(%C%%( ≠=≠= ) !" ! % G !" ! C !" ! ( + C !" ! !" ! ( M E ! ((( M)% M)% ( 2 = MD%LG) MLGD)% σ ( σ !" ! M∈σ M ! ! σ !" ! ! , $ G touscours.net