PLEASE I URGENTLY need your HELP These problems are from my

PLEASE! I URGENTLY need your HELP! These problems are from my Abstract Algebra class:

Fill in the blank (and show your work whenever the answer is not immediate): The order of 4 in U (7) is The order of the group U (28) is The multiplicative inverse of 5 in U(37) is If x epsilon G, x notequalto e, and x^10 = x^35 = e, then |x| = A complete list of generators of the cyclic group Z_14 is The unique subgroup of order 7 in Z_14 is A complete list of elements of order 7 in Z_14 is Let G = (a) and |a| = 20. A complete list of generators for the subgroup of G of order 5 is The subgroup (3) in U(20) is (3) = A complete list of generators of the subgroup (3) in U(20) is

Solution

a) the elemtns to U(7) = {1,2,3,4,5,6}

ord(1)=1

ord(2)=3

ord(3)=6

ord(4)=3

ord(5)=6

ord(6)=2

Therefore order of 4 is 3

b) Given a group GG with order 28=2^27 Sylow-Theory implies that there is a exactly one 77-Sylow-Subgroup of order 7 in GG, and 1 or 7; 2^2-Sylow-Subgroups.

c) the 5 mod of 37 = 17/2

The multiplicative inverse of 5 at 17/2 is 2/17

e) {1, 3, 5, 9, 11, 13}