Let G be a group of order 42 = 2 * 3 * 7
(a) Let P7 be a Sylow 7-subgroup of G and let P3 be a Sylow
3-subgroup of G . What are the orders of P3 and P7?
(b) Prove that P7 is the unique Sylow 7-subgroup of G and that
P7 is normal.
(c) Prove that P3P7 is a subgroup of G
(d) Prove that P3P7 is a normal subgroup of G .
(e) Let P2...
Prove that the cross ratio of four complex numbers z1, z2, z3,
z4 is real if and only if the points z1, z2, z3, z4 lie on a line
or a circle. Then, compute the cross ratio of 1+√ 3, 1−3i, −1 − i
and 1 + i and determine whether they lie on a line, a circle, or
neither.
given z1=2+j3, z2=7+j1, z3=5+j9. find the value of the following
expressions in both coordinate and Euler forms. a)
z1z2,z2z3,z3z3(dash on top z),(z1+z3)z2 b) z1/z2,z2/z3,z3(dash on
to[ z)/z3,(z1+z2)/z3.