Homework Statement
Find 5th roots of unity solving algebraically x^5-1=0. Using the result, find sin18 and cos18The Attempt at a Solution
x^5 = 1\\
x = \sqrt[5]{1}
since we have 5 roots:
x_k, k = 0,1,2,3,4 \\ \\
x_k = e^{i\frac{2k\pi}{n}}, n=5 \\ x_0 = e^{i0} = 1\\ x_1 =...
Homework Statement
Let's say I want to find the inverse of \bar{4} in \mathbb{Z}_{13}.
So I get 13 = 4\cdot 3 + 1 and so 1 = 13 - 4\cdot 3.
But this doesn't show that 3 is inverse of 4. So I have to express 4 = 3\cdot 1 + 1
which yields that 1 = 4 - 1\cdot 3 = 4 - 3\cdot (13 - 3\cdot 4) =...
Direct product of two groups G and H, is the group G\times H = \{ (g,h) | g \in G, h \in H \}.
If * is the operation of G and H, (g,h)*(g_1,h_1) = (g*g_1,h*h_1). Similarly the inverse (g,h)^{-1} = (g^{-1},h^{-1}).
Now can you find any element (g,h) \in \mathbb{Z}_6\times \mathbb{Z}_3 such that...
If H and K are subgroups of G, suppose H⊆K. So we have that |H| divides |K|, and they both divide |G|. If it would happen that |G| = p^ka^r where p, a are different primes, then G would have two subgroups M and N such that |M| divides p, |N| divides a, M ⊄ N and N ⊄ M, thus contradicting the...
Homework Statement
Show that the following conditions are equivalent for a finite group G:
1.G is cyclic and |G| = p^n where p is prime and n\geq 0
2.If H and K are subgroups of G, either H⊆K or K⊆H.
The Attempt at a Solution
1 => 2.
Let H,K be subgroups of G = <g> where o(g)...
Well, you should try to work with classes. As there is no way the program does it automatically for you.
You should learn some OOP, and it will make your life easier when you work with C++.
That's how program's work. They call functions. For example, each time you post something on the forum...