Let F be Field of characteristic 0
L_i (i=1,2) be two algebraic extension
of F , and L_1 L_2 be a field in F^
(where F^ is the algebraic closure of F)
defined by {l_1 l_2 ∣l_i ∈L_i (i=1,2)}
1. show that if L_1 and L_2 are galois over F
then L_1 L_2 is also Galois over F
2. show that if G(L_1 /F^ ) and G(L_2 /F^ )
are Solvable , then Gal(L_1 L_2 /F^ ) is also
Solvable
If A: a_1 , a_2 , ..., a_(62) and B: b_1 , b_2 , ..., b_(62) are two
strictly increasing natural number sequences
such that a_(62) ≤755 and b_(62) ≤755.
Find the maximum of Σ_(i=1) ^(62) ∣a_i −b_i ∣−∣Σ_(i=1) ^(62) (a_i −b_i )∣.