Partiel d`Algèbre

G={a∈R|a > 0, a ̸= 1}a∈G
ln a a G
a∗b=aln(b)
G
2G{e}
G
G
a̸=e G H =< a >
G/H
G2
G:= GL2(Z/5Z)X:= (Z/5Z)2
G×X→X
(g, (x
y))7→ g(x y).
X
(1
0)G
det : G→(Z/5Z)⋆SL2(Z/5Z) :=
ker(det)
Sn{1,· · · , n}
S5S5
2,3,4,5,6S58
10

a:= −I2b:= (1 1
0 1 )∈SL2(Z/5Z)a b
ab
SL2(Z/5Z)S5
S4
F4={Id,(12)(34),(13)(24),(14)(23)}F4
S4
F4
S4
N S4N
F4
M S4
|M|= 12 24
M∩A43
A4F4
S4A4S4